Simplifying square roots: correction of exercises in third grade

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1 Information about this answer key:
2 The exercises in the third grade

Simplify square roots.Corrected third grade math exercises (3ème) on square roots.

Corrected:

We give: $A=\sqrt{300}-4\sqrt{27}+6\sqrt{3}\\B=(5+\sqrt{3})^2\\C=(3\sqrt{2}+\sqrt{5})(3\sqrt{2}-\sqrt{5})$

a) Write A in the form $a\sqrt{3}$ , where a is an integer.

$A=\sqrt{300}-4\sqrt{27}+6\sqrt{3}$

$A=\sqrt{3\times \,100}-4\sqrt{9\times \,3}+6\sqrt{3}$

$A=10\sqrt{3}-4\times \,3\sqrt{3}+6\sqrt{3}$

$A=10\sqrt{3}-12\sqrt{3}+6\sqrt{3}$

${\color{DarkRed}\,A=4\sqrt{3}}$

b) Write B in the form $e+f\sqrt{3}$ with e and f integers.

$B=(5+\sqrt{3})^2$

$B=5^2+2\times \,5\times \,\sqrt{3}+(\sqrt{3})^2$

$B=25+10\,\sqrt{3}+3$

${\color{DarkRed}\,B=28+10\,\sqrt{3}}$

c) Show that C is an integer.

The idea is to use the remarkable identity

$C=\,(\,3\sqrt{2}+\sqrt{5}\,\,)\,(\,3\sqrt{2}-\sqrt{5}\,\,)$

$C=\,(3\sqrt{2})^2-(\sqrt{5})^2$

$C=\,18-5$

${\color{Purple}\,C=\,13}$

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Information about this answer key:

Title:
Simplifying square roots
Correction:

Simplify square roots.Corrected third grade math exercises (3ème) on square roots.

Type:
Answer key to third grade math exercises

Level:
third

The exercises in the third grade

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