How do you simplify $\sqrt{350}$ $sqrt(350)$ ?

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How do you simplify $\sqrt{350}$ $sqrt(350)$ ?

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Answer 1 · 2016-01-07T23:20:23

$5 \sqrt{14}$ $5sqrt14$

Explanation:

search for the factors of $350$ $350$ looking for one that is a perfect square.

In this case $25 \times 14$ $25 xx 14$

$25$ $25$ being the perfect square.

$\sqrt{350} = \sqrt{25 \times 14}$ $sqrt350 = sqrt ( 25 xx 14 )$

now $\sqrt{a b} = \sqrt{a} \times \sqrt{b}$ $sqrt(ab) = sqrta xx sqrtb$ (so long as at least one of $a$ $a$ and $b$ $b$ is not negative)

$\Rightarrow \sqrt{25 \times 14} = \sqrt{25} \times \sqrt{14}$ $rArr sqrt(25 xx 14) = sqrt25 xx sqrt14$

The factors of $14$ $14$ do not contain any square numbers apart from $1$ $1$ and so $\sqrt{14}$ $sqrt14$ cannot be simplified any further.

$\Rightarrow \sqrt{350} = 5 \sqrt{14}$ $rArr sqrt350 = 5sqrt14$

Answer 2 · 2016-01-07T23:51:57

$5 \times \sqrt{14}$ $5timessqrt(14)$

Explanation:

$350 = 35 \times 10 = 7 \times 5 \times 2 \times 5 = 2 \times 5^{2} \times 7$ $350=35times10=7times5times2times5=2times5^2times7$

$\sqrt{350} = \sqrt{2 \times 5^{2} \times 7} = \sqrt{5^{2}} \times \sqrt{2 \times 7} =$ $sqrt(350)=sqrt(2times5^2times7)=sqrt(5^2)timessqrt(2times7)=$

$5 \times \sqrt{2 \times 7} = 5 \times \sqrt{14}$ $5timessqrt(2times7)=5timessqrt(14)$

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How do you simplify $\sqrt{350}$ $sqrt(350)$ ?

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