Question

simplify the following 3 root 16 + 3 root 54 + 3 root 192 minus 3 root 375​

Answer 1

hope this helps you.. :)

Answer 2

The simplified form of the given expression is $5\sqrt[3]{2}+9\sqrt[3]{3}$.

Step-by-step explanation:

Consider the given expression is

$\sqrt[3]{16}+\sqrt[3]{54}+\sqrt[3]{192}+\sqrt[3]{375}$

We need to find the simplified form of the given expression.

The given expression can be rewritten as

$\sqrt[3]{8\times 2}+\sqrt[3]{27\times 2}+\sqrt[3]{64\times 3}+\sqrt[3]{125\times 3}$

$\sqrt[3]{2^3\times 2}+\sqrt[3]{3^3\times 2}+\sqrt[3]{4^3\times 3}+\sqrt[3]{5^3\times 3}$       $[\because \sqrt[a]{x^a}=x]$

On simplification we get

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

On combining like terms we get

$5\sqrt[3]{2}+9\sqrt[3]{3}$

Therefore, the simplified form of the given expression is $5\sqrt[3]{2}+9\sqrt[3]{3}$.

#Learn more

Simplify :

\sqrt[4]{16} - 8 \sqrt[3]{125} +15 \sqrt[5]{32} +  \sqrt{576}

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