Test: Irrational equations

This test develops methods for equations containing square and cube roots. Tasks require students to determine the domain, raise both sides to a power and check for extraneous solutions introduced during transformation.

Question qty: 10
Duration in minutes: 17
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Sample questions

Find the domain of √(x − (a)).
After squaring an irrational equation, a candidate root is obtained. What should be done?
Solve √(x + a) = b.
Solve b√x + (a) = 0.
A square has side s cm. Find its area.
Solve ∛(x³ + b) = ∛v.
Why is checking necessary when solving an irrational equation?

Irrational equations

In an irrational equation, the unknown occurs under a radical. The radicand of an even root must be non-negative, and an isolated square root cannot equal a negative expression.

The risk of squaring

Isolate one radical and square both sides, repeating if necessary. Raising both sides to an even power is not equivalent without sign restrictions and may create extraneous roots. Every candidate must therefore be substituted directly into the original equation.

Test: Irrational equations

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Question Nr. 10 out of 10

Sample questions

Irrational equations

The risk of squaring

Test: Irrational equations

Question Nr. 1 out of 10

Question Nr. 2 out of 10

Question Nr. 3 out of 10

Question Nr. 4 out of 10

Question Nr. 5 out of 10

Question Nr. 6 out of 10

Question Nr. 7 out of 10

Question Nr. 8 out of 10

Question Nr. 9 out of 10

Question Nr. 10 out of 10

Sample questions

Irrational equations

The risk of squaring

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