All questions of Squares & Square Roots for JSS 2 Exam

The answer is 1681 because it is the only number which has it's last digit as a number which a perfect square can have . 9×9=81 the last digit is 1.

Option B is correct because the unit digit of 161 is 1 and if unit digit of any digit ends with 1 the its square will also end with 1.

If a number has 1 or 9 in the unit's place, it means that the number ends with either 1 or 9.

The answer is 1681 because it is the only number which has it's last digit as a number which a perfect square can have . 9×9=81 the last digit is 1.

Square of 60 is 3600 therefore number of zeroes is 2.

Calculation of the Perfect Square:

To find the least number that needs to be added to 4523 to make it a perfect square, we can start by determining the nearest perfect square to 4523.

The square root of 4523 is approximately 67.26. Therefore, the nearest perfect square is 67^2 (4489).

Finding the Difference:

To determine the difference between the nearest perfect square and 4523, we subtract 4489 from 4523:

4523 - 4489 = 34

Finding the Next Perfect Square:

Since the difference is positive, we need to find the next perfect square after 4523. We add twice the square root of 4523 (i.e., 2 * 67.26 ≈ 134.52) plus one to 4523:

4523 + 134.52 + 1 ≈ 4660.52

The square root of 4660.52 is approximately 68.25. Therefore, the next perfect square is 68^2 (4624).

Calculating the Least Number to be Added:

To find the least number to be added to 4523, we subtract 4523 from 4624:

4624 - 4523 = 101

Therefore, the least number that needs to be added to 4523 to make it a perfect square is 101.

Conclusion:

Based on the calculations, the correct answer is option 'A', which is 101.

**Given:**
- Four-fifths of one-eighth of three-fourths of A is 64.

**To find:**
The cube root of three-fifths of A.

**Solution:**
Let's break down the given information step by step.

1. Four-fifths of one-eighth of three-fourths of A is 64.
- Four-fifths of one-eighth: (4/5) * (1/8) = 4/40 = 1/10
- Three-fourths of A: (3/4) * A = 3A/4
- Combining the two: (1/10) * (3A/4) = 3A/40
- So, 3A/40 = 64

2. Solve for A:
- Multiply both sides of the equation by 40 to isolate A: (3A/40) * 40 = 64 * 40
- Simplifying: 3A = 2560
- Divide both sides of the equation by 3 to solve for A: A = 2560/3

3. Find the cube root of three-fifths of A:
- Three-fifths of A: (3/5) * A = (3/5) * (2560/3) = 2560/5 = 512
- Cube root of 512: ∛512 = 8

Therefore, the cube root of three-fifths of A is 8, which corresponds to option B.

Understanding Perfect Squares
A perfect square is a number that can be expressed as the square of an integer. To determine the smallest number by which 180 must be multiplied to become a perfect square, we first need to factor 180 into its prime factors.
Prime Factorization of 180
- The prime factorization of 180 is:
- 180 = 2 × 2 × 3 × 3 × 5
- This can also be written as: 180 = 2^2 × 3^2 × 5^1
Analyzing the Prime Factors
- For a number to be a perfect square, all prime factors must have even exponents.
- In the prime factorization of 180:
- The exponent of 2 is 2 (even)
- The exponent of 3 is 2 (even)
- The exponent of 5 is 1 (odd)
Determining What is Needed
- The only prime factor with an odd exponent is 5.
- To make the exponent of 5 even, we need to multiply by 5.
- Therefore, we need to multiply 180 by 5 to ensure all exponents become even.
Conclusion
- The smallest number by which 180 must be multiplied to become a perfect square is:
- 5
Thus, the correct answer is option 'C'.