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Solving radical equations worksheets Grade 10

Isolate the root, square both sides, solve and check.

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Free · Worked example · 8 problems · Answer key · US Letter

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How to do it

Get the root alone, square both sides, and solve. Check each answer in the original equation.

x+9=x−3x=7\sqrt{x + 9} = x - 3\quad x = 7
x+9=(x−3)2x + 9 = (x - 3)^{2}square both sides
x2−7x=0x^{2} - 7x = 0move every term to one side
(x)(x−7)=0(x)(x - 7) = 0factor
x=0 or x=7x = 0\ \text{or }x = 7set each factor equal to 0
x=0 gives 9=−3, which is false.x = 0\ \text{gives }\sqrt{9} = -3,\ \text{which is false.}check each answer
x=7x = 7

Example problems

  1. x+2=x\sqrt{x + 2} = x
  2. 4x+21−7=0\sqrt{4x + 21} - 7 = 0
  3. x+8=x+2\sqrt{x + 8} = x + 2
  4. x+32−6=0\sqrt{x + 32} - 6 = 0

Exponents, radicals and complex numbers

  1. Zero and negative exponents
  2. Rational exponents
  3. Converting between radicals and rational exponents
  4. Exponent rules with rational exponents
  5. Simplifying cube roots and higher roots
  6. Rationalizing the denominator
  7. Solving radical equations
  8. Imaginary numbers and powers of i
  9. Adding, subtracting and multiplying complex numbers
  10. Dividing complex numbers