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How do you estimate an imperfect square root?

David Jia
Math Tutor
David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.

David Jia

Math Tutor

Expert Answer

If you're trying to find the square root of a number that's not a perfect square, like 80, think about the sqaures that you do know—80 is close to 81, so the answer would have to be close to 9. Then, you could multiply 8.8 times itself to see if that's close. If it's too small, try 8.9.

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Question

What is a square root?

David Jia
Math Tutor
David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.

David Jia

Math Tutor

Expert Answer

Square roots are simply the opposites of squaring. 4 squared is 16, so the square root of 16 is 4.

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What is the number outside of the square root symbol?

Christopher

Top Answerer

Radicals can have any number on the outside. This number indicates which kind of root you're solving for. For example, a 3 indicates a cube root and a 5 indicates a 5th root.

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How can I remember math formulas easily?

Community Answer

Know how those formulas were created or proven. Do them yourself. Or simply, practice writing them down.

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Question

How can I find the square root of 25.72 steps using long division?

Community Answer

To start, 5 squared is 25. So long division of 25.72 divided by 5 gives you 5.144. If you split the difference between 5.144 and 5, that gives you 5.072. 5.072 squared is 25.72.

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What if it doesn't solve the problem?

Community Answer

Try it again, but this time look closely at the numbers you are using, and check your multiples.

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How do I solve problems with addition, subtraction, division, or multiplication of square roots?

Community Answer

Remember the order of operations. Square roots fit into the exponent category, so they're solved just after operations in parentheses. Solve the root, then follow through with the rest of the order of operations.

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Question

What is a square root?

Donagan

Top Answerer

The square root of a number is another number which, when multiplied by itself, gives the first number.

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What is the square root of five plus two root six?

Donagan

Top Answerer

√5 = 2.236. √6 = 2.449. √5 + 2√6 = 2.236 + 2(2.449) = 2.236 + 4.898 = 7.134.

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What is 13 squared -12 squared?

Donagan

Top Answerer

13² - 12² = 169 - 144 = 25.

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Students of a class collected $1225 for the tsunami relief fund. The contribution of each student was as much as the number of students in the class. How many students were there in the class?

Donagan

Top Answerer

Let x be the number of students. Then x also equals the amount of each student's contribution. Then (x)(x) = 1,225, and x = +/-√1225 (and you would reject the negative answer).

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What is a perfect square?

Community Answer

A perfect square means a whole number multiplied by itself. The perfect squares are 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121.

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Question

How do I find the square root of 81x?

Donagan

Top Answerer

√81x = (√81)(√x) = 9√x.

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72/a = a/26. How do I find the value of a?

Donagan

Top Answerer

Cross-multiply to get a² = 1,872. a = +/-√1872.

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What do I do to learn every square root for every number between one and fifty?

Donagan

Top Answerer

The easiest way is to use a "square/square root" table such as the one at MyMathTables.com. Otherwise, use a calculator.

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Solve the square root of 196.

Donagan

Top Answerer

√196 = 14.

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Question

How do I solve 3√12?

Community Answer

3√12 = (3)(3.464) = 10.392. (To find the square root of 12, either use a calculary or see [[Calculate a Square Root by Hand]].)

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Question

How can I find the square root of 0.08?

Community Answer

The easiest way, of course, is to use a calculator. Aside from that, the above article shows other ways of doing it. Basically, you guess a number that, multiplied by itself, will yield 0.08. Perform the multiplication and see how close you come. Then adjust up or down until you arrive at or very near the right number. A calculator will do all that for you instantly.

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What is the square root of √14 - 4√6?

Community Answer

Let's assume you mean √14 - 4√6. That equals 3.74 - (4)(2.45) = 3.74 - 9.80 = -6.06.

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