We read your photo as:

Evaluate the powers of (1)/(sqrt(2)).

May 28, 2026Mathematics

ScanSolve AI Answer

Answer

1 - \sqrt{2}

6 steps

Evaluate the powers of $\frac{1}{\sqrt{2}}$ .
$\left(\frac{1}{\sqrt{2}}\right)^3 = \frac{1^3}{(\sqrt{2})^3} = \frac{1}{2\sqrt{2}}$
Substitute this value back into the expression.
$2\left(\frac{1}{2\sqrt{2}}\right) - 3\left(\frac{1}{\sqrt{2}}\right) + 1$
Simplify the terms.
$\frac{2}{2\sqrt{2}} - \frac{3}{\sqrt{2}} + 1 = \frac{1}{\sqrt{2}} - \frac{3}{\sqrt{2}} + 1$
Combine the fractions.
$\frac{1-3}{\sqrt{2}} + 1 = \frac{-2}{\sqrt{2}} + 1$
Rationalize the denominator of the fraction.
$\frac{-2}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{-2\sqrt{2}}{2} = -\sqrt{2}$
Perform the final addition.
$-\sqrt{2} + 1 = 1 - \sqrt{2}$
The simplified expression is:
$1 - \sqrt{2}$

Was this helpful?

A new problem that tests the same skill.

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.