Basic Math Examples

$1 - \frac{\sqrt{8}}{\sqrt{49}}$

Step 1

Simplify each term.

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Step 1.1

Simplify the numerator.

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Step 1.1.1

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 1.1.1.1

Factor $4$ out of $8$ .

$1 - \frac{\sqrt{4 (2)}}{\sqrt{49}}$

Step 1.1.1.2

Rewrite $4$ as $2^{2}$ .

$1 - \frac{\sqrt{2^{2} \cdot 2}}{\sqrt{49}}$

Step 1.1.2

Pull terms out from under the radical.

$1 - \frac{2 \sqrt{2}}{\sqrt{49}}$

Step 1.2

Simplify the denominator.

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Step 1.2.1

Rewrite $49$ as $7^{2}$ .

$1 - \frac{2 \sqrt{2}}{\sqrt{7^{2}}}$

Step 1.2.2

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

$1 - \frac{2 \sqrt{2}}{7}$

Step 2

Simplify the expression.

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Step 2.1

Write $1$ as a fraction with a common denominator.

$\frac{7}{7} - \frac{2 \sqrt{2}}{7}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{7 - 2 \sqrt{2}}{7}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{7 - 2 \sqrt{2}}{7}$

Decimal Form:

$0.59593898 \dots$