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Sum of squares of two numbers is 145. If square root of one number is 3, find the other number.
- a)136
- b)9
- c)64
- d)8
Correct answer is option 'D'. Can you explain this answer?
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Problem:
The sum of squares of two numbers is 145. If the square root of one number is 3, find the other number.
Solution:
Let's assume the two numbers as x and y.
Given:
x^2 + y^2 = 145 ........(1)
√x = 3
Now let's solve the problem step by step:
Step 1: Find the value of x
We are given that the square root of x is 3. So, we can write it as:
√x = 3
Squaring both sides of the equation, we get:
(√x)^2 = 3^2
x = 9
Therefore, the value of x is 9.
Step 2: Substitute the value of x in equation (1)
Now that we have the value of x, we can substitute it in equation (1) and solve for y:
9^2 + y^2 = 145
81 + y^2 = 145
Subtracting 81 from both sides, we get:
y^2 = 64
Taking the square root of both sides, we get:
√y^2 = √64
y = 8
Therefore, the value of y is 8.
Step 3: Find the other number
We have found the values of x and y as 9 and 8 respectively. Now we need to find the other number, which is y.
So, the other number is 8.
Conclusion:
The other number is 8. Therefore, the correct answer is option D.
The sum of squares of two numbers is 145. If the square root of one number is 3, find the other number.
Solution:
Let's assume the two numbers as x and y.
Given:
x^2 + y^2 = 145 ........(1)
√x = 3
Now let's solve the problem step by step:
Step 1: Find the value of x
We are given that the square root of x is 3. So, we can write it as:
√x = 3
Squaring both sides of the equation, we get:
(√x)^2 = 3^2
x = 9
Therefore, the value of x is 9.
Step 2: Substitute the value of x in equation (1)
Now that we have the value of x, we can substitute it in equation (1) and solve for y:
9^2 + y^2 = 145
81 + y^2 = 145
Subtracting 81 from both sides, we get:
y^2 = 64
Taking the square root of both sides, we get:
√y^2 = √64
y = 8
Therefore, the value of y is 8.
Step 3: Find the other number
We have found the values of x and y as 9 and 8 respectively. Now we need to find the other number, which is y.
So, the other number is 8.
Conclusion:
The other number is 8. Therefore, the correct answer is option D.
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Sum of squares of two numbers is 145. If square root of one number is 3, find the other number.a)136b)9c)64d)8Correct answer is option 'D'. Can you explain this answer?
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