Math Problem Statement

\left(\sqrt{5-\sqrt3}\right) $$$$ ^2

Solution

The expression you provided is:

(53)2\left(\sqrt{5 - \sqrt{3}}\right)^2

When you square a square root, the square root and the square cancel out. So, we can simplify this as:

(53)2=53\left(\sqrt{5 - \sqrt{3}}\right)^2 = 5 - \sqrt{3}

Thus, the simplified form is:

535 - \sqrt{3}

Would you like further details or have any other questions?

Here are 5 related questions for further practice:

  1. Simplify (7+2)2\left(\sqrt{7 + \sqrt{2}}\right)^2.
  2. Simplify 9+5×95\sqrt{9 + \sqrt{5}} \times \sqrt{9 - \sqrt{5}}.
  3. Simplify (4+3)2\left(\sqrt{4 + \sqrt{3}}\right)^2.
  4. Expand (a+b)2(a + b)^2 for any values of aa and bb.
  5. Solve for xx if x=106x = \sqrt{10 - \sqrt{6}}.

Tip: When squaring a square root, remember that the square and the square root cancel each other out.

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Math Problem Analysis

Mathematical Concepts

Algebra
Square Roots
Exponents

Formulas

(\sqrt{a})^2 = a

Theorems

Simplification of square roots

Suitable Grade Level

Grades 9-10