Solve sqrt{10}-sqrt{5}(sqrt{10}-sqrt{5})

$$\sqrt{ 10 } - \sqrt{ 5 } ( \sqrt{ 10 } - \sqrt{ 5 } )$$

Evaluate

$$\sqrt{10}+5-5\sqrt{2}\approx 1.091209848$$

Solution Steps

Use the distributive property to multiply \sqrt{5} by \sqrt{10}-\sqrt{5}.

$$\sqrt{10}-\left(\sqrt{5}\sqrt{10}-\left(\sqrt{5}\right)^{2}\right)$$

Factor 10=5\times 2. Rewrite the square root of the product \sqrt{5\times 2} as the product of square roots \sqrt{5}\sqrt{2}.

$$\sqrt{10}-\left(\sqrt{5}\sqrt{5}\sqrt{2}-\left(\sqrt{5}\right)^{2}\right)$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\sqrt{10}-\left(5\sqrt{2}-\left(\sqrt{5}\right)^{2}\right)$$

The square of \sqrt{5} is 5.

$$\sqrt{10}-\left(5\sqrt{2}-5\right)$$

To find the opposite of 5\sqrt{2}-5, find the opposite of each term.

$$\sqrt{10}-5\sqrt{2}-\left(-5\right)$$

The opposite of -5 is 5.

$$\sqrt{10}-5\sqrt{2}+5$$