What is the square root of 1600?
The Correct Answer and Explanation is:
Correct 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 (squared), gives the original number. In other words, if x2=1600x^2 = 1600×2=1600, then xxx is the square root of 1600.
We start by trying to simplify 1600. Notice that 1600 ends in two zeros, which tells us it is a perfect square of a number ending in zero. Let’s rewrite 1600 as a product of its prime factors to better understand it.
Start by dividing 1600 by small prime numbers:1600÷2=800800÷2=400400÷2=200200÷2=100100÷2=5050÷2=2525÷5=55÷5=11600 \div 2 = 800 \\ 800 \div 2 = 400 \\ 400 \div 2 = 200 \\ 200 \div 2 = 100 \\ 100 \div 2 = 50 \\ 50 \div 2 = 25 \\ 25 \div 5 = 5 \\ 5 \div 5 = 11600÷2=800800÷2=400400÷2=200200÷2=100100÷2=5050÷2=2525÷5=55÷5=1
So the prime factorization of 1600 is:1600=26×521600 = 2^6 \times 5^21600=26×52
To find the square root, we take half the exponents of the prime factors:1600=26×52=26/2×52/2=23×51=8×5=40\sqrt{1600} = \sqrt{2^6 \times 5^2} = 2^{6/2} \times 5^{2/2} = 2^3 \times 5^1 = 8 \times 5 = 401600=26×52=26/2×52/2=23×51=8×5=40
Thus, the square root of 1600 is 40.
We can verify this by squaring 40:40×40=160040 \times 40 = 160040×40=1600
This confirms our result.
Also, recognizing perfect squares can help. Since:402=1600and1600=40×4040^2 = 1600 \quad \text{and} \quad 1600 = 40 \times 40402=1600and1600=40×40
we conclude that 40 is the positive square root of 1600.
In summary, the square root of 1600 is 40, because 40 multiplied by itself equals 1600.
