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# Simplify

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Simplify sqrt(27)*sqrt(12)*sqrt(147).

Apr 28, 2023

#1
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Simplify sqrt(27)*sqrt(12)*sqrt(147).

This expression is equivalent to the

sqrt of the product of the radicands

sqrt(27) * sqrt(12) * sqrt(147)               =   sqrt( 27 * 12 * 147 )

See if you can find some

perfect squares in there                        =   sqrt( 3*9 * 3*4 * 147 )

There are two 32 and one 22

so take them out from under

the radical                                              =   (3 * 3 * 2) sqrt( 147 )

=   18 * sqrt(147)

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Apr 28, 2023
#2
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CONTINUED FROM ABOVE

too late to edit my above

I noticed another square

SUBSTITUTE THE FOLLOWING

See if you can find some

perfect squares in there                        =   sqrt( 3*9 * 3*4 * 3*49 )

There are two 32, one 22,

and one 72, so take them

out from under the radical                     =   (3 * 3 * 2 * 7) sqrt( 3 )

=  126 * sqrt(3)

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Guest Apr 28, 2023
#3
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126$$\sqrt{3}$$

So we know that:

$$\sqrt{27} * \sqrt{(12)} * \sqrt{(147)}$$

( ' * ' being " multiply " )

= 42 $$\sqrt{3}^3$$

Simplify:

= 42 * 3$$\sqrt{3}$$

Multiply:

42 * 3 $$\sqrt{3}$$

= 126$$\sqrt{3}$$

Apr 28, 2023