Find the square root. 1600′
The Correct Answer and Explanation is:
Answer:
The square root of 1600 is 40.
Explanation
To find the square root of a number means to determine what number, when multiplied by itself, equals the original number. In mathematical terms, ifx2=1600,x^2 = 1600,x2=1600,
thenx=1600.x = \sqrt{1600}.x=1600.
Let’s go step-by-step.
First, recognize that 1600 is a perfect square, meaning it is the product of an integer multiplied by itself. To confirm this, factor 1600 to see if it can be written as the square of a whole number.
Start by simplifying:1600=16×1001600 = 16 \times 1001600=16×100
Both 16 and 100 are perfect squares:
- 16=4\sqrt{16} = 416=4
- 100=10\sqrt{100} = 10100=10
Now apply the square root to each factor:1600=16×100=16×100=4×10=40\sqrt{1600} = \sqrt{16 \times 100} = \sqrt{16} \times \sqrt{100} = 4 \times 10 = 401600=16×100=16×100=4×10=40
Thus,1600=40\sqrt{1600} = 401600=40
This means that 40 × 40 = 1600. When checking square roots, always multiply the result by itself to verify that it returns the original number:40×40=160040 \times 40 = 160040×40=1600
This confirms the answer is correct.
Additional Tip:
To determine whether a number is a perfect square, factor it and look for repeated prime factors or break it into known square numbers. For example:1600=26×521600 = 2^6 \times 5^21600=26×52
To take the square root, divide each exponent by 2:26×52=23×5=8×5=40\sqrt{2^6 \times 5^2} = 2^3 \times 5 = 8 \times 5 = 4026×52=23×5=8×5=40
This is another way to verify that the square root of 1600 is 40.
