(628)-272-0788 info@etutorworld.com

Approximating Square Roots

Approximating Square Roots

The ‘square root’ of a given positive number ‘n’ is that number which, when multiplied by itself, gives ‘n’.

If the square root of a given number is not a whole number, then we can approximate the square root of a number.

approximating square roots

 Square Roots of Perfect Squares

\\sqrt{1} 1
\\sqrt{4} 2
\\sqrt{9} 3
\\sqrt{16} 4
\\sqrt{25} 5
\\sqrt{36} 6
\\sqrt{49} 7
\\sqrt{64} 8
\\sqrt{81} 9
\\sqrt{100} 10
\\sqrt{121} 11
\\sqrt{144} 12

 

Steps to approximate square roots:

Step 1: Think of two perfect squares between which the given number lies.

Example: If we want to find the square root of 12, then 32 = 9 and 42 = 16. So, \\sqrt{12} lies between 9 and 16.

Step 2: Divide the given number by one of the two square roots in step 1.

12 ÷ 3 = 4

Step 3: Find the average of the root and the result in step 2.

\\frac{4 + 3}{{2}}=\\frac{7}{{2}} =3.5

Step 4: Repeat steps 2 and 3 until you reach the desired result.

Repetition of step 2: 12 ÷ 3.5 = 3.4285

Repetition of step 3: =\\frac{3.4285+3.5}{{2}}=\\frac{6.9285}{{2}}= 3.46425

Now you need to decide the level accuracy to find the square root of given number. If you want it to be more accurate, keep on repeating steps 2 and 3. We leave \\sqrt{12}  here.

CHECK POINT

Find the square root of the given numbers, rounded to the nearest tenth.

  1.  \\sqrt{165}
  2.  \\sqrt{189}
  3.   \\sqrt{44}
  4.  \\sqrt{103}
  5.  \\sqrt{114}
Answer key
  1.  12.8
  2.  13.7
  3.  6.6
  4.  10.1
  5.  10.7

eTutorWorld Understands Math Tutoring | Online Math Worksheets are Important Tools

Understanding graphs, charts, and opinion polls in a newspaper, for calculating house and car payments, and for choosing a long-distance telephone service are impossible without strong math skills …and the only way to develop strong math skills is by constant practice.

‘Practice makes a man perfect’ holds true for no other field better than for math. A middle or high school student must set aside a minimum of an hour for math every day. Other than textbooks, worksheets help you revise and understand concepts better.

Our expert tutors prepare online maths worksheets that are age and grade-appropriate. Grade-wise math worksheets for Elementary Math, Arithmetic, Pre-Algebra, Algebra, Geometry, Trigonometry, Statistics, Pre-Calculus and Calculus can be solved to improve math skills, to get ahead or to even catch up.

You may download these FREE online math worksheets in the PDF format, and then print and email us their solutions for a free evaluation and analysis by eTutorworld’smath expert tutors.

You may solve these worksheets by yourself or with your peers while studying together.

The Answer Key at the end of each worksheet allows for a self-evaluation.

Personalized Online Tutoring

eTutorWorld offers affordable one-on-one live tutoring over the web for Grades K-12, Test Prep help for Standardized tests like SCAT, CogAT, MAP, SSAT, SAT, ACT, ISEE and AP. You may schedule online tutoring lessons at your personal scheduled times, all with a Money-Back Guarantee. The first one-on-one online tutoring lesson is always FREE, no purchase obligation, no credit card required.

For answers/solutions to any question or to learn concepts, take a FREE CLASS.

No credit card required, no obligation to purchase.
Just book a free class to meet a tutor and get help on any topic you want!

Pricing for Online Tutoring

Tutoring Package Validity Grade (1-12), College
5 sessions 1 Month $139
1 session 1 Month $28
10 sessions 3 months $269
15 sessions 3 months $399
20 sessions 4 months $499
50 sessions 6 months $1189
100 sessions 12 months $2249