Simplify fourth root of 11*4 square root of 10

$\sqrt[4]{11} \cdot 4 \sqrt{10}$

Step 1

Multiply $\sqrt[4]{11} (4 \sqrt{10})$ .

Rewrite the expression using the least common index of $4$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10}$ as $10^{\frac{1}{2}}$ .

$4 (\sqrt[4]{11} \cdot 10^{\frac{1}{2}})$

Rewrite $10^{\frac{1}{2}}$ as $10^{\frac{2}{4}}$ .

$4 (\sqrt[4]{11} \cdot 10^{\frac{2}{4}})$

Rewrite $10^{\frac{2}{4}}$ as $\sqrt[4]{10^{2}}$ .

$4 (\sqrt[4]{11} \sqrt[4]{10^{2}})$

Combine using the product rule for radicals.

$4 \sqrt[4]{11 \cdot 10^{2}}$

Step 2

Rewrite $11 \cdot 10^{2}$ as $0.11 \cdot 10^{4}$ .

$4 \sqrt[4]{0.11 \cdot 10^{4}}$

Step 3

Rewrite $\sqrt[4]{0.11 \cdot 10^{4}}$ as $\sqrt[4]{0.11} \cdot \sqrt[4]{10^{4}}$ .

$4 (\sqrt[4]{0.11} \cdot \sqrt[4]{10^{4}})$

Step 4

Evaluate the root.

$4 (0.57590144 \cdot \sqrt[4]{10^{4}})$

Step 5

Pull terms out from under the radical, assuming positive real numbers.

$4 (0.57590144 \cdot 10)$

Step 6

Raise $10$ to the power of $1$ .

$4 \cdot 0.57590144 \cdot 10^{1}$

Step 7

Multiply $4$ by $0.57590144$ .

$2.30360579 \cdot 10^{1}$

Step 8

The result can be shown in multiple forms.

Scientific Notation:

$2.30360579 \cdot 10^{1}$

Expanded Form:

$23.03605796$