Worksheet: Solving Quadratic Equations: Taking Square Roots

In this worksheet, we will practice solving quadratic equations with no linear term using the square root property.

Q1:

Find the solution set of the equation (π‘₯βˆ’17)=0 in ℝ.

  • A{βˆ’17}
  • B{289}
  • C{17}
  • D{17,βˆ’17}

Q2:

Find the solution set of the equation 3π‘₯βˆ’44=0 in ℝ, giving values to one decimal place.

  • A{8.1,βˆ’8.1}
  • B{βˆ’14.7,14.7}
  • C{23.0,βˆ’23.0}
  • D{3.8,βˆ’3.8}

Q3:

Solve π‘₯=2.

  • Aπ‘₯=4
  • Bπ‘₯=√2, π‘₯=βˆ’βˆš2
  • Cπ‘₯=2, π‘₯=βˆ’2
  • Dπ‘₯=√2
  • Eπ‘₯=2

Q4:

Solve the equation π‘₯+1=√3.

  • Aπ‘₯=ο„βˆš3βˆ’1
  • Bπ‘₯=ο„βˆš3+1, π‘₯=βˆ’ο„βˆš3+1
  • Cπ‘₯=ο„βˆš3βˆ’1, π‘₯=βˆ’ο„βˆš3βˆ’1
  • Dπ‘₯=ο„βˆš3, π‘₯=βˆ’ο„βˆš3
  • Eπ‘₯=βˆ’ο„βˆš3βˆ’1

Q5:

Solve π‘₯=511.

  • Aπ‘₯=ο„ž115
  • Bπ‘₯=ο„ž511
  • Cπ‘₯=√511, π‘₯=βˆ’βˆš511
  • Dπ‘₯=ο„ž115, π‘₯=βˆ’ο„ž115
  • Eπ‘₯=ο„ž511, π‘₯=βˆ’ο„ž511

Q6:

Solve the equation π‘₯=16.

  • Aπ‘₯=4, π‘₯=βˆ’4
  • Bπ‘₯=8, π‘₯=βˆ’8
  • Cπ‘₯=8
  • Dπ‘₯=4
  • Eπ‘₯=βˆ’4

Q7:

Solve (π‘₯+6)=4.

  • Aπ‘₯=βˆ’4 or π‘₯=βˆ’8
  • Bπ‘₯=8 or π‘₯=βˆ’8
  • Cπ‘₯=βˆ’5 or π‘₯=βˆ’7
  • Dπ‘₯=7 or π‘₯=5
  • Eπ‘₯=8 or π‘₯=4

Q8:

Solve the equation π‘₯+2=√3.

  • Aπ‘₯=βˆ’ο€Ώο„2βˆ’βˆš3𝑖
  • Bπ‘₯=2βˆ’βˆš3𝑖, π‘₯=βˆ’ο€Ώο„2βˆ’βˆš3𝑖
  • Cπ‘₯=2βˆ’βˆš3𝑖
  • Dπ‘₯=ο„βˆš3βˆ’2, π‘₯=βˆ’ο„βˆš3βˆ’2
  • Eπ‘₯=√3βˆ’22, π‘₯=βˆ’βˆš3βˆ’22

Q9:

Solve the equation (π‘₯βˆ’2)=7.

  • Aπ‘₯=9
  • Bπ‘₯=3, π‘₯=βˆ’3
  • Cπ‘₯=2+√7, π‘₯=2βˆ’βˆš7
  • Dπ‘₯=2+√7
  • Eπ‘₯=2βˆ’βˆš7

Q10:

Solve π‘₯+5=12.

  • Aπ‘₯=√17
  • Bπ‘₯=√12βˆ’5
  • Cπ‘₯=√7
  • Dπ‘₯=√17, π‘₯=βˆ’βˆš17
  • Eπ‘₯=√7, π‘₯=βˆ’βˆš7

Q11:

Determine the solution set of the equation 44π‘₯+9=0 given that π‘₯βˆˆβ„.

  • Aβˆ…
  • B3√1122
  • Cο―βˆ’3√1122
  • Dο―βˆ’3√1122,3√1122

Q12:

Given that π‘₯=ο€»βˆš13βˆ’βˆš11ο‡ο€»βˆš13+√11ο‡οŠ¨, find the possible values of π‘₯.

  • A2√6
  • B√2
  • C√2,βˆ’βˆš2
  • D2√6,βˆ’2√6

Q13:

Find all the possible values of π‘₯ for which 2π‘₯=50.

  • A√5,βˆ’βˆš5
  • B10
  • C5,βˆ’5
  • D25

Q14:

Find all the values of π‘₯ which satisfy π‘₯3=48π‘₯.

  • A144
  • B12
  • C12,βˆ’12
  • Dβˆ’12
  • E144,βˆ’144

Q15:

Solve π‘₯=4.

  • Aπ‘₯=8 or π‘₯=βˆ’8
  • Bπ‘₯=16 or π‘₯=βˆ’16
  • Cπ‘₯=2
  • Dπ‘₯=8
  • Eπ‘₯=2 or π‘₯=βˆ’2

Q16:

Solve π‘₯+5=14.

  • Aπ‘₯=2
  • Bπ‘₯=9 or π‘₯=βˆ’9
  • Cπ‘₯=3
  • Dπ‘₯=9
  • Eπ‘₯=3 or π‘₯=βˆ’3

Q17:

Find the solution set of the equation (π‘₯βˆ’5)=100 in β„š.

  • Aβˆ…
  • B{15}
  • C{βˆ’15,5}
  • D{βˆ’5,15}

Q18:

Solve π‘₯=916.

  • Aπ‘₯=316 or π‘₯=βˆ’316
  • Bπ‘₯=316
  • Cπ‘₯=94 or π‘₯=βˆ’94
  • Dπ‘₯=34 or π‘₯=βˆ’34
  • Eπ‘₯=34

Q19:

Given that 9π‘₯+2=4, find the value of π‘₯, and state whether it is a rational or irrational number.

  • A±√63, rational number
  • B±√23, rational number
  • C±√23, irrational number
  • D±√63, irrational number
  • EΒ±29, irrational number

Q20:

Write all of the values of π‘₯ which satisfy the equation 2π‘₯+8=13οŠͺ. If necessary, give your answer(s) to 4 significant figures.

  • A1.5
  • B1.257
  • C12.57,βˆ’12.57
  • Dβˆ’1.257
  • E1.257,βˆ’1.257

Q21:

Find the solution set of the equation π‘₯=145 given that π‘₯βˆˆβ„.

  • A√70,βˆ’βˆš70
  • B√705
  • C√7014,βˆ’βˆš7014
  • D√705,βˆ’βˆš705
  • E√7014

Q22:

Solve π‘₯=0.36.

  • Aπ‘₯=0.36 or π‘₯=βˆ’0.36
  • Bπ‘₯=0.06 or π‘₯=βˆ’0.06
  • Cπ‘₯=6 or π‘₯=βˆ’6
  • Dπ‘₯=36 or π‘₯=βˆ’36
  • Eπ‘₯=0.6 or π‘₯=βˆ’0.6

Q23:

Find the solution set of (π‘₯+1)βˆ’64=0 in ℝ.

  • A{βˆ’21,3}
  • B{βˆ’9,7}
  • C{βˆ’1,1}
  • D{βˆ’7,9}
  • E{βˆ’3,21}

Q24:

If ο€Ήπ‘₯βˆ’5,8=ο€Ί95,βˆšπ‘¦ο†οŠ¨οŽ’, find all the possible values of π‘₯ and 𝑦.

  • Aπ‘₯=10, 𝑦=8
  • Bπ‘₯=10 or π‘₯=βˆ’10, 𝑦=512
  • Cπ‘₯=100, 𝑦=512
  • Dπ‘₯=10 or π‘₯=βˆ’10, 𝑦=8

Q25:

Find the solution set of the equation 4π‘₯=π‘₯9.

  • A{6}
  • B{36}
  • C{6,βˆ’6}
  • D{4,9}
  • E{36,βˆ’36}

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