Question

simplify
2 ³√4 + 7 ³√32 –³√500​

Answer 1

2* ( 4)^ 1/3 + 7 * (4)^1/3 (8) ^1/3 - (4) ^1/3 *( 125) ^1/3
(4) ^1/3 [ 2+7 *2 -5]
(4) ^1/3 [ 11]
11 * (2) ^2/3

Answer 2

$2\sqrt[3]{4}+7\sqrt[3]{32}-\sqrt[3]{500}=11\sqrt[3]{4}$

Step-by-step explanation:

Given : Expression $2\sqrt[3]{4}+7\sqrt[3]{32}-\sqrt[3]{500}$

To find : Simplify the expression ?

Solution :

Expression $2\sqrt[3]{4}+7\sqrt[3]{32}-\sqrt[3]{500}$

where values can be written as,

$32=2\times 2\times 2\times 2\times 2$

i.e. $\sqrt[3]{32}=2\times \sqrt[3]{4}$

$500=4\times 5\times 5\times 5$

i.e. $\sqrt[3]{500}=5\times \sqrt[3]{4}$

Substitute in the equation,

$=2\sqrt[3]{4}+7(2\sqrt[3]{4})-5\sqrt[3]{4}$

$=2\sqrt[3]{4}+14\sqrt[3]{4}-5\sqrt[3]{4}$

$=\sqrt[3]{4}(2+14-5)$

$=11\sqrt[3]{4}$

Therefore, $2\sqrt[3]{4}+7\sqrt[3]{32}-\sqrt[3]{500}=11\sqrt[3]{4}$

#Learn more

Simplify: √(3+2√2)

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