square roots, 10th grade math test.

This proctored assignment is intended for teachers or students who want to review the chapter on square roots in 10th grade. In order to do well, you will have to start by reading the statement in its entirety. This will allow you to have a good overview of the subject and to avoid making calculation errors when solving the exercises. The chapter on square roots is very important and mastering it will help you grow well in math. Use all the materials allowed to make your calculations easier. This test will allow you to practice first but then to see if you have assimilated this chapter on square roots.

The teacher will also have the opportunity to grade his or her students and go over any misunderstood parts of the chapter with them at the end of the math test. Also, always stay focused and think carefully before starting an exercise.

Ex 1: Course Questions.

1) Give the definition of the square root of a positive number a.

2) Quote the course properties related to the square root of a product and quotient of numbers.

3) Give a counterexample showing that there is no formula for the sum.

Ex 2 : Direct application of the course.

Write in integer form, detailing the calculations.

$A=\frac{\sqrt{27}}{\sqrt{3}}\\B=\frac{\sqrt{7}\times ,\sqrt{13}}{\sqrt{91}}\\C=\sqrt{32}\times ,\sqrt{2}\\D=\sqrt{\frac{121}{144}}\\E=\sqrt{36+64}$

Ex 3 : Brevet type exercises .

We consider $F=2\sqrt{5}+\sqrt{125}-6\sqrt{45}\,et\,,G=\sqrt{8}+\sqrt{50}-\sqrt{18}$

1) Write G and F in the form $a\sqrt{b}$ , a and b being two integers, b being the smallest possible.

2) Using a calculation, show that the number $H=(3\sqrt{2}+3)(\sqrt{2}-1)$ is a whole number.

3) Develop: $I=(2-3\sqrt{2})^2$ and express the result in the form $a+b\sqrt{5}$ with a and b relative integers.

Ex 4 : Brevet type exercises .

Consider a triangle XYZ such that XY = $\sqrt{3}-1$ ; XZ = $\sqrt{8}$ and ZY = $\sqrt{3}+1$ (in cm).

Is XYZ a rectangle?

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