RD Sharma Solutions for Class 8 Math Chapter 3 - Squares and Square Roots (Part-6) | RD Sharma Solutions for Class 8 Mathematics PDF Download

Question 1: Find the square root in decimal form:
84.8241

Answer 1: 

Hence, the square root of 84.8241 is 9.21. 

Question 2: Find the square root in decimal form:
0.7225

Answer 2:

Hence, the square root of 0.7225 is 0.85. 

Question 3: Find the square root in decimal form:
0.813604

Answer 3:

Hence, the square root of 0.813604 is 0.902. 

Question 4: Find the square root in decimal form:0.00002025

Answer 4:

 

Hence, the square root of 0.00002025 is 0.0045. 

Question 5: Find the square root in decimal form:
150.0625

Answer 5: 

Hence, the square root of 150.0625 is 12.25. 

Question 6: Find the square root in decimal form:
225.6004

Answer 6:

Hence, the square root of 225.6004 is 15.02 

Question 7: Find the square root in decimal form:
3600.720036

Answer 7:

Hence, the square root of 3600.720036 is 60.006. 

Question 8: Find the square root in decimal form:
236.144689

Answer 8: 

Hence, the square root of 236.144689 is 15.367. 

Question 9: Find the square root in decimal form:
0.00059049

Answer 9:

Hence, the square root of 0.00059049 is 0.0243. 

Question 10: Find the square root in decimal form:
176.252176

Answer 10:

Hence, the square root of 176.252176 is 13.276.

Question 11: Find the square root in decimal form:
9998.0001

Answer 11:

 

Hence, the square root of 9998.0001 is 99.99. 

Question 12: Find the square root in decimal form:
0.00038809

Answer 12:

Hence, the square root of 0.00038809 is 0.0197. 

Question 13: What is that fraction which when multiplied by itself gives 227.798649?

Answer 13: We have to find the square root of the given number.

Hence, the fraction, which when multiplied by itself, gives 227.798649 is 15.093. 

Question 14: The area of a square playground is 256.6404 square metres. Find the length of one side of the playground.

Answer 14: The length of one side of the playground is the square root of its area.

So, the length of one side of the playground is 16.02 metres. 

Question 15: What is the fraction which when multiplied by itself gives 0.00053361?

Answer 15: We have to find the square root of the given number. 

Hence, the fraction, which when multiplied by itself, gives 0.00053361 is 0.0231. 

Question 16: Simplify:

Answer 16: (i) We have:

 

(ii) We have: 

  =0.48 

=0.42 

Question 17: Evaluate 50625 and hence find the value of

Answer 17: We have: 
  =3×3×5×5=225

Next, we will calculate 

 =22.5 

 =2.25

  22.5+2.25=24.75 

Question 18: Find the value of  and hence find the value of

Answer 18: The value of 103.0225 is: 

Hence, the square root of 103.0225 is 10.15.
Now, we can solve the following questions as shown below:

(i)  10.15×10=101.5  

(ii)  
=1.015 

Question 19: Find the square root of each of the following correct to three places of decimal.
(i) 5
(ii) 7
(iii) 17
(iv) 20
(v) 66
(vi) 427
(vii) 1.7
(viii) 23.1
(ix) 2.5
(x) 237.615
(xi) 15.3215
(xii) 0.9
(xiii) 0.1
(xiv) 0.016
(xv) 0.00064
(xvi) 0.019

(xvii) 7/8

(xviii)  5/12

(xix)  

(xx)

Answer 19: (i) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places. 

Hence, the square root of 5 up to three decimal places is 2.236.
(ii) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 7 up to three decimal places is 2.646.
(iii) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 17 up to three decimal places is 4.123.
(iv) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 20 up to three decimal places is 4.472.
(v) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 66 up to three decimal places is 8.124.
(vi) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 427 up to three decimal places is 20.664.
(vii) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 1.7 up to three decimal places is 1.304.
(viii) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 23.1 up to three decimal places is 4.806.
(ix) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 2.5 up to three decimal places is 1.581.
(x) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 237.615 up to three decimal places is 15.415.
(xi) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 15.3215 up to three decimal places is 3.914.
(xii) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 0.9 up to three decimal places is 0.949.
(xiii) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 0.1 up to three decimal places is 0.316.
(xiv) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 0.016 up to three decimal places is 0.126.
(xv) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 0.00064 up to three decimal places is 0.025.
(xvi) We can find the square root up to three decimal places by using long division until we get four decimal places and then rounding it to three decimal places.

Hence, the square root of 0.019 up to three decimal places is 0.138.
(xvii) We can find the square root up to four decimal places by expanding 7/8 to decimal form up to eight digits to the right of the decimal point as shown below:
7/8=0.87578=0.875
Hence, we have:

So, the square root of 7/8 up to three decimal places is 0.935.
(xviii) We can find the square root up to four decimal places by expanding 5/12 to decimal form up to eight digits to the right of the decimal point as shown below:

Hence, we have:

So, the square root of 5/12 up to three decimal places is 0.645.
(xix) We can find the square root up to four decimal places by expanding  into decimal form up to eight digits to the right of the decimal point as shown below:
=2.50000000212=2.50000000
But, this is the same with the value 2.5 in problem (ix). Hence, the square root of    is 1.581.
(xx) We can find the square root up to four decimal places by expanding 28758 into decimal form up to eight digits to the right of the decimal point as shown below:
=287.62500000
Hence, we have:

So, the square root of   up to three decimal places is 16.960.