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

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Answer 1 · 2017-04-13T00:01:31

#-98sqrt3#

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#