Radical Expressions and Equations Quiz

Grade 10 · Math · Quiz

Test your skills simplifying radicals, performing operations, and solving radical equations.

Questions

Which is the simplified form of √50?
1. 5√2
2. 10√5
3. 25√2
4. 5√10
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Answer: 5√2
√50 = √(25·2) = 5√2. 25 is the largest perfect square factor of 50.
2√3 + 2√5 = 4√8.
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Answer: False
You can only add radicals with the same radicand. √3 ≠ √5, so these cannot be combined. 4√8 is not equivalent.
√12 · √3 = √___ = 6.
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Answer: 36
√12 · √3 = √(12·3) = √36 = 6.
Rationalize: 4/√2 =
1. 2√2
2. 4√2
3. 2/√2
4. √8
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Answer: 2√2
4/√2 × √2/√2 = 4√2/2 = 2√2.
Solve √(2x - 1) = 3. What is x?
1. x = 4
2. x = 5
3. x = 10
4. x = 2
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Answer: x = 5
Square both sides: 2x-1=9 → 2x=10 → x=5. Check: √(10-1)=√9=3 ✓.
x^(1/3) is the same as the cube root of x.
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Answer: True
By definition, x^(1/n) = ⁿ√x. So x^(1/3) = ∛x, the cube root of x.
Simplify: √75 - √27
1. 5√3 - 3√3 = 2√3
2. √48
3. √3
4. 4√3
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Answer: 5√3 - 3√3 = 2√3
√75=√(25·3)=5√3; √27=√(9·3)=3√3. Subtracting: 5√3-3√3=2√3.
x^(m/n) equals (ⁿ√x)^___.
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Answer: m
x^(m/n) = (ⁿ√x)^m. The denominator n is the index of the root; the numerator m is the exponent.
√(-9) has a real number answer.
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Answer: False
Square roots of negative numbers are not real numbers; they are imaginary (involving i = √(-1)).
Which step is critical after solving a radical equation by squaring?
1. Factor both sides
2. Check for extraneous solutions
3. Simplify the radical again
4. Find the LCD
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Answer: Check for extraneous solutions
Squaring can create extraneous solutions. Always substitute back into the original equation to verify every answer.

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