Pre-Algebra Examples

$\sqrt{250000 - \sqrt{90000}}$

Step 1

Rewrite $90000$ as $300^{2}$ .

$\sqrt{250000 - \sqrt{300^{2}}}$

Step 2

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

$\sqrt{250000 - 1 \cdot 300}$

Step 3

Multiply $- 1$ by $300$ .

$\sqrt{250000 - 300}$

Step 4

Subtract $300$ from $250000$ .

$\sqrt{249700}$

Step 5

Rewrite $249700$ as $10^{2} \cdot 2497$ .

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Step 5.1

Factor $100$ out of $249700$ .

$\sqrt{100 (2497)}$

Step 5.2

Rewrite $100$ as $10^{2}$ .

$\sqrt{10^{2} \cdot 2497}$

Step 6

Pull terms out from under the radical.

$10 \sqrt{2497}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$10 \sqrt{2497}$

Decimal Form:

$499.69990994 \dots$