Math Problem Statement

(√2 - √3)^2 = ? A. 5 - 2√6 B. 5 - √6 C. 1 - 2√6 D. 1 - √2 E. 1

Solution

The image contains a mathematical expression that needs to be solved. The question appears to be:

(23)2\left( \sqrt{2} - \sqrt{3} \right)^2

The possible answers provided are:

A. 5265 - 2\sqrt{6}
B. 565 - \sqrt{6}
C. 1261 - 2\sqrt{6}
D. 121 - \sqrt{2}
E. 1

Let's expand the given expression and simplify it:

(23)2=(2)22(2×3)+(3)2\left( \sqrt{2} - \sqrt{3} \right)^2 = \left( \sqrt{2} \right)^2 - 2\left( \sqrt{2} \times \sqrt{3} \right) + \left( \sqrt{3} \right)^2

First, calculate each term:

  1. (2)2=2\left( \sqrt{2} \right)^2 = 2
  2. (3)2=3\left( \sqrt{3} \right)^2 = 3
  3. 2×2×3=2×6-2 \times \sqrt{2} \times \sqrt{3} = -2 \times \sqrt{6}

Thus, the expanded form is:

2+326=5262 + 3 - 2\sqrt{6} = 5 - 2\sqrt{6}

Therefore, the correct answer is A.

Would you like any further details or clarification on this solution?

Here are 5 related questions:

  1. How do you expand binomials like (ab)2(a - b)^2?
  2. What is the rule for multiplying square roots, like 2×3\sqrt{2} \times \sqrt{3}?
  3. Can you apply the same steps for (5+7)2(\sqrt{5} + \sqrt{7})^2?
  4. How does simplifying surds (like 6\sqrt{6}) work in general?
  5. Why is the middle term 2×2×3-2 \times \sqrt{2} \times \sqrt{3} rather than something else?

Tip: Always remember to apply the distributive property carefully when squaring binomials involving roots.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Exponents and Radicals
Binomial Expansion

Formulas

(a - b)^2 = a^2 - 2ab + b^2

Theorems

Distributive Property
Simplification of Radicals

Suitable Grade Level

Grades 9-11