Question

express the surds in the simplest form i] square root 8 ii]cube root 192

Answer 1

SOLUTION

TO DETERMINE

Express the surds in the simplest form

$\sf{(i) \: \: \: \sqrt{8} }$

$\sf{(ii) \: \: \: \sqrt[3]{192} }$

EVALUATION

ANSWER TO QUESTION :

$\sf{ \sqrt{8} }$

$\sf{ = \sqrt{2 \times 2 \times 2} }$

$\sf{ = \sqrt{ {2}^{2} \times 2} }$

$\sf{ =2 \sqrt{ 2} }$

ANSWER TO QUESTION : 2

$\sf{ \sqrt[3]{192} }$

$\sf{ = \sqrt[3]{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3} }$

$\sf{ = \sqrt[3]{ {2}^{3} \times {2}^{3} \times 3} }$

$\sf{ = \sqrt[3]{ {(2 \times 2)}^{3} \times 3} }$

$\sf{ = \sqrt[3]{ {4}^{3} \times 3} }$

$\sf{ = 4 \sqrt[3]{ 3} }$

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