What is the exact value of the square root of 32 over 5 the square root of 14?

Question

1185 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-06T03:27:23

$(4sqrt7)/35$

$sqrt32/(5sqrt14)$

Simplify $sqrt32$ .

$sqrt(2xx2xx2xx2xx2)/(5sqrt14)=$

$sqrt(2^2xx2^2xx2)/(5sqrt14)=$

Apply square root rule $sqrt(a^2)=a$ .

$(2xx2sqrt(2))/(5sqrt14)=$

$(4sqrt2)/(5sqrt14)$

Rationalize the denominator.

$(4sqrt2)/(5sqrt14)xx(sqrt14)/sqrt14=$

$(4sqrt2sqrt14)/(5xx14)=$

$(4sqrt28)/70=$

Simplify $(4sqrt28)$ .

$(4sqrt(2xx2xx7))/70=$

$(4sqrt(2^2xx7))/70=$

$(4xx2sqrt7)/70=$

$(8sqrt7)/70$

Simplify.

$(4sqrt7)/35$