Math Problem Statement

leave as a surd : 4 root 3 divided by root 2

Solution

To leave the expression 432\frac{4 \sqrt{3}}{\sqrt{2}} in surd form, we can simplify it by rationalizing the denominator.

  1. Multiply both the numerator and denominator by 2\sqrt{2} to get rid of the surd in the denominator: 432×22=43×22×2=462\frac{4 \sqrt{3}}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{4 \sqrt{3} \times \sqrt{2}}{\sqrt{2} \times \sqrt{2}} = \frac{4 \sqrt{6}}{2}

  2. Now, simplify the fraction: 462=26\frac{4 \sqrt{6}}{2} = 2 \sqrt{6}

Thus, 432\frac{4 \sqrt{3}}{\sqrt{2}} in surd form is 262 \sqrt{6}.

Would you like more details or have any questions?

Here are five related questions for practice:

  1. Simplify 523\frac{5 \sqrt{2}}{\sqrt{3}}.
  2. Simplify 357\frac{3 \sqrt{5}}{\sqrt{7}}.
  3. What is 122\frac{\sqrt{12}}{\sqrt{2}} in surd form?
  4. Simplify 684\frac{6 \sqrt{8}}{\sqrt{4}}.
  5. Rationalize the denominator of 75\frac{\sqrt{7}}{\sqrt{5}}.

Tip: When simplifying expressions with surds, rationalizing the denominator is a helpful technique to eliminate square roots from the denominator.

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Math Problem Analysis

Mathematical Concepts

Surds
Rationalization of Denominators
Simplification of Radicals

Formulas

\( \frac{a \sqrt{b}}{\sqrt{c}} \times \frac{\sqrt{c}}{\sqrt{c}} = \frac{a \sqrt{bc}}{c} \)

Theorems

Rationalization of Surds
Simplification of Square Roots

Suitable Grade Level

Grades 8-10