What is the square root of 5 times the square root of 35?

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Answer 1 · 2018-05-30T12:20:28

What is: $sqrt(5) xx sqrt(35)$ ?

Use this rule for radicals to combine the terms:

$sqrt(color(red)(a)) * sqrt(color(blue)(b)) = sqrt(color(red)(a) * color(blue)(b))$

$sqrt(color(red)(5)) * sqrt(color(blue)(35)) => sqrt(color(red)(5) * color(blue)(35)) => sqrt(175)$

Next, we can rewrite the term under the radical as:

$sqrt(25 * 7)$

Now, use this rule for radicals to simplify the expression:

$sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))$

$sqrt(color(red)(25) xx color(blue)(7)) => sqrt(color(red)(25)) xx sqrt(color(blue)(7)) => 5 xx sqrt(7) => 5sqrt(7)$

Answer 2 · 2018-05-30T12:21:26

$5sqrt(7)$

$sqrt(5)*sqrt(35)=sqrt(5*35)=sqrt(175)$

Note that we now have among the factors of 175 a square under the square root that we can take out to simplify

$sqrt(175)=sqrt(5^2*7)=5sqrt(7)*$

It is usually worth keeping track of what factors go in in advance - so in this case remembering that $35=5*7$ .