Q&A for How to Solve Square Root Problems

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  • Question
    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.
    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.
  • 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.
    Math Tutor
    Expert Answer
    Square roots are simply the opposites of squaring. 4 squared is 16, so the square root of 16 is 4.
  • Question
    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.
  • Question
    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.
  • 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.
  • Question
    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.
  • Question
    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.
  • 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.
  • Question
    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.
  • Question
    What is 13 squared -12 squared?
    Donagan
    Top Answerer
    13² - 12² = 169 - 144 = 25.
  • Question
    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).
  • Question
    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.
  • Question
    How do I find the square root of 81x?
    Donagan
    Top Answerer
    √81x = (√81)(√x) = 9√x.
  • Question
    72/a = a/26. How do I find the value of a?
    Donagan
    Top Answerer
    Cross-multiply to get a² = 1,872. a = +/-√1872.
  • Question
    Solve the square root of 196.
    Donagan
    Top Answerer
    √196 = 14.
  • Question
    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.
  • 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]].)
  • 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.
  • Question
    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.
  • Question
    25×4=3×5×2=30. Is that the correct answer?
    I_l1ke_gam3s
    Community Answer
    25 x 4 = 100. If you want here's a way to do it mentally: 25 x 2 = 50. You then would have to double the 50. 50 + 50 = 100. As for 3x5x2=30, you would be correct. But 25x4's answer being equivalent to the 3x5x2, that statement would be false.
  • Question
    What is the square of 16⅖?
    Community Answer
    (16 2/5)² = (82/5)² = 6724/25 = 268 24/25.
  • Question
    How do you solve the square for 17?
    I_l1ke_gam3s
    Community Answer
    If you're asking for the square root of 17, it's 4.123. If you meant 17 squared, that's 289.
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