Question
Download Solution PDFThe sum of two numbers is 28 and the sum of their squares is 528. Find the square root of the product of both the numbers.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The sum of two numbers is 28.
The sum of their squares is 528.
Formula Used:
(a + b) = a^2 + b^2 + 2ab
Calculation:
Let the two numbers be a and b.
a + b = 28
a2 + b2 = 528
We know:
(a + b)2 = a2 + b2 + 2ab
Substitute the given values:
⇒ (28)2 = 528 + 2ab
⇒ 784 = 528 + 2ab
⇒ 784 - 528 = 2ab
⇒ 256 = 2ab
⇒ ab = 128
We need to find the square root of the product of both numbers:
√(ab) = √128
√128 = √(64 × 2)
√128 = 8√2
The square root of the product of both the numbers is 8√2.
Last updated on May 28, 2025
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