Simplifying square roots

$50$ isn't a whole number, but it does hide a square. Since $50 = 25 \cdot 2$ , and $ab = a b$ , we can take the 25 out as a 5.

50 = 52

Work through it

Find the biggest square factor. $72 = 36 \cdot 2$

Take its root out. $62$

Simplify each. $23 + 33$

Same root, so combine. $53$

A square root is the exponent $\frac{1}{2}$ . Add exponents. $x^{2}$

$9 + 16 = 3 + 4$ .

Roots don't split over addition. $25 = 5$ , not 7.

The short version
Find the largest perfect square that divides the number. It comes out as its root.

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