Gr 10 Math Ch 1: Estimating Surds

Which of the following is an example of a surd?

4

3

√2 (correct)

1.5

What is the nearest perfect square to estimate √15?

25

4

16 (correct)

9 (correct)

If 2 < x < 3, which of the following must be true regarding \sqrt{x}?

2 < √x < 3

1 < √x < 2

√2 < √x < √3 (correct)

0 < √x < 3

What is the value of √16?

4 Signup and view all the answers

Identify the statement that correctly describes surds.

Surds are roots of integers that cannot be simplified to rational numbers. Signup and view all the answers

Which of the following statements about surds is true?

Surds are the n-th root of numbers that cannot be simplified to rational numbers. Signup and view all the answers

Which numbers are typically used to estimate surds?

Perfect squares or cubes surrounding the surd. Signup and view all the answers

If \sqrt{a} < 4 and \sqrt{b} < 8, what can be inferred about a and b?

a is less than 16 and b is less than 64. Signup and view all the answers

Which of the following best describes how to estimate the value of \sqrt{5}?

Estimate using the perfect square 4, as it is the closest lower perfect square. Signup and view all the answers

Which of the following inequalities represents the relationship between two surds considering the root properties?

\sqrt{4} < \sqrt{5} < \sqrt{6} Signup and view all the answers

Which statement accurately defines a surd?

The n-th root of a number that cannot be simplified to a rational number. Signup and view all the answers

What is the correct method to estimate the value of \sqrt{20}?

Identify that \sqrt{16} = 4 and \sqrt{25} = 5, then interpolate. Signup and view all the answers

If \sqrt{a} < \sqrt{9} and \sqrt{b} > \sqrt{4}, what can be inferred about the values of a and b?

a is less than 9 and b is greater than or equal to 4. Signup and view all the answers

What principle is used to compare two surds, \sqrt[n]{a} and \sqrt[n]{b}?

If a < b, then \sqrt[n]{a} < \sqrt[n]{b}. Signup and view all the answers

How does one identify the closest perfect cube when estimating \sqrt[3]{30}?

Estimate using the perfect cubes of 8 and 27. Signup and view all the answers

Gr 10 Math Ch 1: Estimating Surds

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