Basic Math Examples

$4 \sqrt{75 \cdot \sqrt{27}}$

Step 1

Rewrite $27$ as $3^{2} \cdot 3$ .

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Step 1.1

Factor $9$ out of $27$ .

$4 \sqrt{75 \sqrt{9 (3)}}$

Step 1.2

Rewrite $9$ as $3^{2}$ .

$4 \sqrt{75 \sqrt{3^{2} \cdot 3}}$

$4 \sqrt{75 \sqrt{3^{2} \cdot 3}}$

Step 2

Pull terms out from under the radical.

$4 \sqrt{75 \cdot 3 \sqrt{3}}$

Step 3

Write the expression using exponents.

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Step 3.1

Multiply $75$ by $3$ .

$4 \sqrt{225 \sqrt{3}}$

Step 3.2

Rewrite $225$ as $15^{2}$ .

$4 \sqrt{15^{2} \sqrt{3}}$

$4 \sqrt{15^{2} \sqrt{3}}$

Step 4

Pull terms out from under the radical.

$4 (15 \sqrt{\sqrt{3}})$

Step 5

Rewrite $\sqrt{\sqrt{3}}$ as $\sqrt[4]{3}$ .

$4 (15 \sqrt[4]{3})$

Step 6

Multiply $15$ by $4$ .

$60 \sqrt[4]{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$60 \sqrt[4]{3}$

Decimal Form:

$78.96444077 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$