How do you simplify: the square root of 200?

Jul 27, 2015

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Explanation:

• Square root of a number can be simplified by prime factorising the number.

• Prime factorisation involves expressing a number as a product of prime numbers.

($200$ has $2$ and $5$ as its prime factors.)

So,

$\sqrt{200} = \sqrt{2 \cdot 2 \cdot 2 \cdot 5 \cdot 5}$

$\sqrt{200} = \sqrt{{2}^{2} \cdot 2 \cdot {5}^{2}}$

$= 2 \cdot 5 \sqrt{2}$

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