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Radicals - MYP Questionbank | RevisionDojo

Practice Radicals with authentic MYP MYP Standard Mathematics exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of MYP examiners.

Type

Difficulty

Question 1

Simplify the expression $\sqrt{27} - \sqrt{12}$ .

Question 2

Without using a calculator, determine which of the following statements is correct.

Question 3

If $x$ is an irrational number, which of the following expressions is guaranteed to also be an irrational number?

Question 4

Which of the following statements about the number $\sqrt{\frac{4}{5}}$ is correct?

Question 5

Which of the following numerical statements serves as a counterexample to prove that $\sqrt{a - b} = \sqrt{a} - \sqrt{b}$ is NOT a valid general rule?

Question 6

Which of the following statements correctly describes the result of the product $\sqrt{2} \cdot \sqrt{8}$ ?

Question 7

True or False: The sum of any two irrational numbers is always another irrational number.

Question 8

Using the quotient rule for radicals, find the exact value of the expression: $\frac{\sqrt{20}}{\sqrt{5}}$

Question 9

True or False: For any two positive real numbers $a$ and $b$ , the identity $\sqrt{a+b} = \sqrt{a} + \sqrt{b}$ is always true.

Question 10

Simplify $\sqrt{72}$ to its simplest radical form.

Type

Difficulty

Question 1

Simplify the expression $\sqrt{27} - \sqrt{12}$ .

Question 2

Without using a calculator, determine which of the following statements is correct.

Question 3

If $x$ is an irrational number, which of the following expressions is guaranteed to also be an irrational number?

Question 4

Which of the following statements about the number $\sqrt{\frac{4}{5}}$ is correct?

Question 5

Which of the following numerical statements serves as a counterexample to prove that $\sqrt{a - b} = \sqrt{a} - \sqrt{b}$ is NOT a valid general rule?

Question 6

Which of the following statements correctly describes the result of the product $\sqrt{2} \cdot \sqrt{8}$ ?

Question 7

True or False: The sum of any two irrational numbers is always another irrational number.

Question 8

Using the quotient rule for radicals, find the exact value of the expression: $\frac{\sqrt{20}}{\sqrt{5}}$

Question 9

True or False: For any two positive real numbers $a$ and $b$ , the identity $\sqrt{a+b} = \sqrt{a} + \sqrt{b}$ is always true.

Question 10

Simplify $\sqrt{72}$ to its simplest radical form.

Type

Difficulty

Question 1

Simplify the expression $\sqrt{27} - \sqrt{12}$ .

Question 2

Without using a calculator, determine which of the following statements is correct.

Question 3

If $x$ is an irrational number, which of the following expressions is guaranteed to also be an irrational number?

Question 4

Which of the following statements about the number $\sqrt{\frac{4}{5}}$ is correct?

Question 5

Which of the following numerical statements serves as a counterexample to prove that $\sqrt{a - b} = \sqrt{a} - \sqrt{b}$ is NOT a valid general rule?

Question 6

Which of the following statements correctly describes the result of the product $\sqrt{2} \cdot \sqrt{8}$ ?

Question 7

True or False: The sum of any two irrational numbers is always another irrational number.

Question 8

Using the quotient rule for radicals, find the exact value of the expression: $\frac{\sqrt{20}}{\sqrt{5}}$

Question 9

True or False: For any two positive real numbers $a$ and $b$ , the identity $\sqrt{a+b} = \sqrt{a} + \sqrt{b}$ is always true.

Question 10

Simplify $\sqrt{72}$ to its simplest radical form.

Radicals Questionbank