Dolly Robinson

2020-11-14

To calculate: The simplified value of the radical expression $\sqrt{18a}\xf7\sqrt{2{a}^{4}}.$

unett

Skilled2020-11-15Added 119 answers

Given expression is $\sqrt{18a}\xf7\sqrt{2{a}^{4}}.$

Formula used:

The product rule for radicals,

$\sqrt[n]{a}b=\sqrt[n]{a}\cdot \sqrt[n]{b}$

Here, n is the positive integer and a and b are real number.

The relation between radical and rational exponent notation is expressed as,

$\sqrt[n]{a}={a}^{1\text{/}n}.$

Here, a is the radicand, and n is the index of the radical.

Calculation:

Consider the given expression,

$\sqrt{18a}\xf7\sqrt{2{a}^{4}}.$

Use the product rule for radicals to simplify the expression,

$\sqrt{18a}\xf7\sqrt{2{a}^{4}}=\frac{\sqrt{18a}}{\sqrt{2{a}^{4}}}$

$=\frac{\sqrt{9\cdot 2\cdot a}}{\sqrt{2}\cdot {a}^{2}\cdot {a}^{2}}$

$=\frac{\sqrt{{3}^{2}}\cdot \sqrt{2}\cdot \sqrt{a}}{\sqrt{2}\cdot \sqrt{{a}^{2}\cdot \sqrt{{a}^{2}}}}$

Use the relation between radical and rational exponent notation to simplify the expression,

$\sqrt{18a}\xf7\sqrt{2{a}^{4}}=\frac{{\left({3}^{2}\right)}^{1\text{/}2}\sqrt{a}}{{\left({a}^{2}\right)}^{1\text{/}2}{\left({a}^{2}\right)}^{1\text{/}2}}$

$=\frac{{\left(3\right)}^{2\left(1\text{/}2\right)}\sqrt{a}}{{\left(a\right)}^{2\left(1\text{/}2\right)}{\left(a\right)}^{2\left(1\text{/}2\right)}}$

$=\frac{\left(3\right)\sqrt{a}}{\left(a\right)\left(a\right)}$

$=\frac{3\sqrt{a}}{{n}^{2}}$

Hence, the simplified value of the provided expression is$\frac{3\sqrt{a}}{{a}^{2}}.$

Formula used:

The product rule for radicals,

Here, n is the positive integer and a and b are real number.

The relation between radical and rational exponent notation is expressed as,

Here, a is the radicand, and n is the index of the radical.

Calculation:

Consider the given expression,

Use the product rule for radicals to simplify the expression,

Use the relation between radical and rational exponent notation to simplify the expression,

Hence, the simplified value of the provided expression is

Jeffrey Jordon

Expert2021-10-25Added 2605 answers

Answer is given below (on video)

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