Question

How do you simplify `sqrt21*sqrt24`?

Answer 1

`\sqrt(21)*\sqrt(24)=6*\sqrt(14)`

Explanation:

`\sqrt(21)*\sqrt(24)=`
`=\sqrt(21*24)=\sqrt(3*7*3*8)=\sqrt(3^2*7*2*2^2)=`
`=3*2*\sqrt(2*7)=6*\sqrt(14)`

Answer 2

`6sqrt14`

Explanation:

`"using the "color(blue)"law of radicals"`

`•color(white)(x)sqrtaxxsqrtbhArrsqrt(ab)`

`"simplifying "sqrt24=sqrt(4xx6)=sqrt4xxsqrt6=2sqrt6`

`rArrsqrt21xx2sqrt6=2sqrt126`

`=2sqrt(9xx14)=2(sqrt9xxsqrt14)=2(3sqrt14)=6sqrt14`