find the value of square root of 50625 and hence find the value of square root of 506.25 + 5.0625
The correct answer and explanation is:
Correct Answer:
- √50625 = 225
- √506.25 + 5.0625 = 22.5 + 5.0625 = 27.5625
Full Explanation (300 words):
To solve this problem, we begin by finding the square root of 50625.
Start with:
√50625
Check if 50625 is a perfect square. Since 225² = 50625, then:
√50625 = 225
Now that we know the square root of 50625, we can use this to help solve the second part:
√506.25 + 5.0625
We note that 506.25 is 50625 ÷ 100. This is because shifting the decimal two places to the left divides the number by 100. Therefore:
√506.25 = √(50625 ÷ 100) = √50625 ÷ √100 = 225 ÷ 10 = 22.5
So,
√506.25 = 22.5
Now add:
22.5 + 5.0625 = 27.5625
This gives the final answer for the expression:
√506.25 + 5.0625 = 27.5625
Why this method works:
The square root of a number tells you what value multiplied by itself gives the original number. In the case of 50625, it is a perfect square, so its root is a whole number. Breaking down 506.25 into 50625 ÷ 100 lets us use our earlier result efficiently. Since the square root of a quotient is the same as the quotient of the square roots, we simplify √506.25 by dividing √50625 by √100.
Adding 5.0625 to this root is straightforward since both are decimal numbers. This approach saves time and avoids unnecessary decimal approximations. Always check if numbers can be rewritten in forms that use known square roots to simplify calculations quickly and accurately.