Simplify (1.96*4)÷( square root of 50)

$1.96 \cdot 4 \div \sqrt{50}$

Step 1

Rewrite the division as a fraction.

$\frac{1.96 \cdot 4}{\sqrt{50}}$

Step 2

Multiply $1.96$ by $4$ .

$\frac{7.84}{\sqrt{50}}$

Step 3

Simplify the denominator.

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$\frac{7.84}{\sqrt{25 (2)}}$

Rewrite $25$ as $5^{2}$ .

$\frac{7.84}{\sqrt{5^{2} \cdot 2}}$

Pull terms out from under the radical.

$\frac{7.84}{5 \sqrt{2}}$

Step 4

Multiply $\frac{7.84}{5 \sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{7.84}{5 \sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}$

Step 5

Combine and simplify the denominator.

Multiply $\frac{7.84}{5 \sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\frac{7.84 \sqrt{2}}{5 \sqrt{2} \sqrt{2}}$

Move $\sqrt{2}$ .

$\frac{7.84 \sqrt{2}}{5 (\sqrt{2} \sqrt{2})}$

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{7.84 \sqrt{2}}{5 ({\sqrt{2}}^{1} \sqrt{2})}$

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{7.84 \sqrt{2}}{5 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{7.84 \sqrt{2}}{5 {\sqrt{2}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{7.84 \sqrt{2}}{5 {\sqrt{2}}^{2}}$

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

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

$\frac{7.84 \sqrt{2}}{5 {(2^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{7.84 \sqrt{2}}{5 \cdot 2^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{7.84 \sqrt{2}}{5 \cdot 2^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{7.84 \sqrt{2}}{5 \cdot 2^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{7.84 \sqrt{2}}{5 \cdot 2^{1}}$

Evaluate the exponent.

$\frac{7.84 \sqrt{2}}{5 \cdot 2}$

Step 6

Multiply $7.84$ by $\sqrt{2}$ .

$\frac{11.08743432}{5 \cdot 2}$

Step 7

Simplify the expression.

Multiply $5$ by $2$ .

$\frac{11.08743432}{10}$

Divide $11.08743432$ by $10$ .

$1.10874343$

Simplify (1.96*4)÷( square root of 50)

Related Questions