Question

What is the square root of 98 minus, square root of 24 plus the square root of 32?

Answer 1

`11*sqrt(2)-2*sqrt(6)`

Explanation:

`sqrt(98)=sqrt(2*49)=sqrt(2)*7`
`sqrt(24)=sqrt(6*4)=2sqrt(6)`
`sqrt(32)=sqrt(2*16)=4*sqrt(2)`

Answer 2

`11sqrt(2)-2sqrt(6)`

Explanation:

`sqrt(98) = sqrt(2xx7xx7)=7sqrt(2)`
`sqrt(24) = sqrt(2xx2xx2xx3)=2sqrt(6)`
`sqrt(32) = sqrt(2xx2xx2xx2xx2)=4sqrt(2)`

`7sqrt(2)-2sqrt(6)+4sqrt(2)=11sqrt(2)-2sqrt(6)`

Answer 3

`11sqrt2-2sqrt6`

Explanation:

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

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

`"simplifying each radical gives"`

`sqrt98=sqrt(49xx2)=sqrt49xxsqrt2=7sqrt2`

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

`sqrt32=sqrt(16xx2)=sqrt16xxsqrt2=4sqrt2`

`rArrsqrt98-sqrt24+sqrt32`

`=color(blue)(7sqrt2)-2sqrt6color(blue)(+4sqrt2)`

`=11sqrt2-2sqrt6`