How do you simplify -7\sqrt { 21} \cdot \sqrt { 28}?

1 Answer
Apr 13, 2017

-98sqrt3

Explanation:

When adding or subtracting radicals, they have to be the same.

When mutliplying however, the rule does not apply.

So for -7sqrt21*sqrt28, we first try to expand the radicals and see if any of them will give us a simpler value.

sqrt21 =sqrt7*sqrt3

sqrt28=sqrt7*sqrt4

Thus,

-7xx(sqrt7*sqrt3)xx(sqrt7*sqrt4)

Group like terms to make simplification easier

-7xxsqrt7xxsqrt7xxsqrt4xxsqrt3

Note,

sqrt7xxsqrt7=7

How???

(color(red)sqrt7)^(color(red)2)=7

So we have,

-7xx7xxsqrt4xxsqrt3

We know that,

sqrt4=2

Leaving us with

-7xx7xx2xxsqrt3

-49xx2xxsqrt3

-98*sqrt3

sqrt3 cannot be simplified to give a whole number.

Thus, our answer is

rArr-98sqrt3