Expand? ${(a^{2} + b^{2})}^{\frac{3}{2}}$ $(a^2+b^2)^(3/2)$

Question

Expand? ${(a^{2} + b^{2})}^{\frac{3}{2}}$ $(a^2+b^2)^(3/2)$

1 Answer

Impact of this question

1793 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-06T15:35:53

$(a^{2} + b^{2}) \sqrt{a^{2} + b^{2}}$ $(a^2+b^2)sqrt(a^2+b^2)$

Explanation:

${(a^{2} + b^{2})}^{\frac{3}{2}}$ $(a^2+b^2)^(3/2)$

The fractional power $\frac{3}{2}$ $3/2$ says that we're going to cube the expression (the 3) and then take the square root (the 2). So let's do that:

$\sqrt{(a^{2} + b^{2}) (a^{2} + b^{2}) (a^{2} + b^{2})}$ $sqrt((a^2+b^2)(a^2+b^2)(a^2+b^2))$

Since $(a^{2} + b^{2}) (a^{2} + b^{2}) = {(a^{2} + b^{2})}^{2}$ $(a^2+b^2)(a^2+b^2)=(a^2+b^2)^2$ , we can write:

$\sqrt{{(a^{2} + b^{2})}^{2} (a^{2} + b^{2})}$ $sqrt((a^2+b^2)^2(a^2+b^2))$

taking the square root:

$(a^{2} + b^{2}) \sqrt{a^{2} + b^{2}}$ $(a^2+b^2)sqrt(a^2+b^2)$

Can we go further than this? No - the addition of the $a^{2}$ $a^2$ and $b^{2}$ $b^2$ terms means we can't simply take the square root of each piece.

Science

Math

Humanities

... and beyond

Expand? ${(a^{2} + b^{2})}^{\frac{3}{2}}$ $(a^2+b^2)^(3/2)$

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

Expand? (a2+b2)32(a^2+b^2)^(3/2)

1 Answer

Explanation:

Related questions

Impact of this question

Expand? ${(a^{2} + b^{2})}^{\frac{3}{2}}$ $(a^2+b^2)^(3/2)$