How do you find the square root of 5625?

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How do you find the square root of 5625?

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Answer 1 · 2015-09-08T21:26:34

Split into prime factors, identify factors which occur in pairs, hence find: $5625 = 75^{2}$ $5625 = 75^2$ , so:

$\sqrt{5625} = 75$ $sqrt(5625) = 75$

Explanation:

Start by finding prime factors of $5625$ $5625$ :

$2$ $2$ : No: $5625$ $5625$ is odd.
$3$ $3$ : Yes:
$X X 5625 = 3 \cdot 1875 = 3 \cdot 3 \cdot 625$ $color(white)(XX)5625 = 3 * 1875 = 3 * 3 * 625$
$5$ $5$ : Yes:
$X X 3 \cdot 3 \cdot 625 = 3 \cdot 3 \cdot 5 \cdot 125 = 3 \cdot 3 \cdot 5 \cdot 5 \cdot 25$ $color(white)(XX)3 * 3 * 625 = 3 * 3 * 5 * 125 = 3 * 3 * 5 * 5 * 25$
$X X = 3 \cdot 3 \cdot 5 \cdot 5 \cdot 5 \cdot 5 = {(3 \cdot 5 \cdot 5)}^{2} = 75^{2}$ $color(white)(XX)= 3 * 3 * 5 * 5 * 5 * 5 = (3*5*5)^2 = 75^2$

Answer 2 · 2018-07-03T19:59:35

$\sqrt{5625} = 75$ $sqrt5625=75$

Explanation:

As the number ends with $25 = 5^{2}$ $25 =5^2$ , 5625, therefore, is a multiplum of 25.

I also recognise that $25^{2} = 625$ $25^2=625$ , which is the last part of 5625. I would, therefore, check if 5625 is a multiplum of 625:
$\frac{5625}{625} = 9 = 3^{2}$ $5625/625=9=3^2$

Therefore $5625 = 3^{2} \cdot 25^{2} = 75^{2}$ $5625=3^2*25^2=75^2$

Therefore $\sqrt{5625} = 75$ $sqrt5625=75$

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How do you find the square root of 5625?

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