Evaluate square root of 40- square root of 10+ square root of 90

$\sqrt{40} - \sqrt{10} + \sqrt{90}$

Step 1

Simplify each term.

Rewrite $40$ as $2^{2} \cdot 10$ .

Factor $4$ out of $40$ .

$\sqrt{4 (10)} - \sqrt{10} + \sqrt{90}$

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

$\sqrt{2^{2} \cdot 10} - \sqrt{10} + \sqrt{90}$

$\sqrt{2^{2} \cdot 10} - \sqrt{10} + \sqrt{90}$

Pull terms out from under the radical.

$2 \sqrt{10} - \sqrt{10} + \sqrt{90}$

Rewrite $90$ as $3^{2} \cdot 10$ .

Factor $9$ out of $90$ .

$2 \sqrt{10} - \sqrt{10} + \sqrt{9 (10)}$

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

$2 \sqrt{10} - \sqrt{10} + \sqrt{3^{2} \cdot 10}$

$2 \sqrt{10} - \sqrt{10} + \sqrt{3^{2} \cdot 10}$

Pull terms out from under the radical.

$2 \sqrt{10} - \sqrt{10} + 3 \sqrt{10}$

$2 \sqrt{10} - \sqrt{10} + 3 \sqrt{10}$

Step 2

Simplify by adding terms.

Subtract $\sqrt{10}$ from $2 \sqrt{10}$ .

$\sqrt{10} + 3 \sqrt{10}$

Add $\sqrt{10}$ and $3 \sqrt{10}$ .

$4 \sqrt{10}$

$4 \sqrt{10}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{10}$

Decimal Form:

$12.64911064 \dots$

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