Question

Answer these questions

Answer 1

Here is your answer.

Question number b:-

$\sqrt{2} (6 + 2 \sqrt{2} )$

$= 6 \sqrt{2} + 4$

Question number c:-

$\sqrt{7} (2 + 3 \sqrt{7} )$

$= 2 \sqrt{7} + 21$

Question number d:-

$\sqrt{2} ( \sqrt{32} - \sqrt{8} )$

$= \sqrt{64} - \sqrt{16}$

$= 8 - 4$

$= 4$

Answer 2

1) √2(6+2√2)

$\red{ \sf{ \sqrt{2} (6 + 2 \sqrt{2} )}}$

$\sf multiply \: each \: \underline {\orange { term}} \: in \: the \: parantheses \: by \sqrt{2}$

$\red{ \sf{ 6 \sqrt{2} + \sqrt{2} \times2 \sqrt{2} }}$

${ \sf{ 6 \sqrt{2} + \red{ \sqrt{2} \times2 \sqrt{2} }}}$

$\sf calculate \: the \: {\orange {\underline{product.}}}$

$6 \sqrt{2} + \red{ 4}$

$\sf \red{solution}$

$6 \sqrt{2 } + 4$

$\sf \red{alternate \: form}$

$≈12.48528$

2) √7(2+3√7)

$\red{ \sf{ \sqrt{7} (2 + 3 \sqrt{7} )}}$

$\sf multiply \: each \: \underline {\orange { term}} \: in \: the \: parantheses \: by \sqrt{7}$

$\red{ \sf{ 2\sqrt{7} + \sqrt{7} \times3 \sqrt{7} }}$

${ \sf{ 2\sqrt{7} + \red{ \sqrt{7} \times3 \sqrt{7} }}}$

$\sf calculate \: the \: {\orange {\underline{product.}}}$

$2 \sqrt{7} + \red{ 21}$

$\sf \red{solution}$

$2 \sqrt{7} + 21$

$\sf \red{alternate \: form}$

$≈26.2915$

3) √2(√32-√8)

$\sqrt{2} ( \red{ \sqrt{32} - \sqrt{8}} )$

$\sf simplfy \: the \: \orange {\underline{ radical \: expression}}$

$\sqrt{2} ( \red{ 4 \sqrt{2} - 2 \sqrt{2} } )$

$\sf collect \: \orange {\underline{ like \: terms}}$

$\sqrt{2} \times \red{ 2 \sqrt{2} }$

$\red{\sqrt{2} }\times 2 \red{ \sqrt{2} }$

$\sf when \: a \: \orange {\underline{ square \: root}} \: of \: an \: expression \\ \sf is \: multiplied \: by \: itself, \: the \: result \\ \sf is \: that \: expression.$

$\red{2 }\times 2$

$\red{2 \times 2}$

$\sf multiply \: terms$

$\red{4}$

$\sf \red{solution}$

$4$