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Last updated on December 2nd, 2024
When someone asks you to explain a square root, you can just tell that it is a number when multiplied by itself produces the same number. As we continue with our explanation, let’s assume the value of 78 Here 78 is considered as a non-perfect square root since it contain either decimal or fraction. Let's learn more about square roots in this article.
The square root of 78 can be easily found out by using long division method. In which it is discovered that the cumulative approximation of √78 is 8.831.
There are many ways through which students can find square roots, and some of these methods are very popular. Some of the methods have been explained in detail below.
In this method, we decompose the number into its prime factors.
Prime factorization of 78: 78 = 2×3×13.
Since not all prime factors can be paired, 78 cannot be simplified into a perfect square. Therefore, the square root of 78 cannot be expressed in a simple radical form.
For non-perfect squares, we often use the nearest perfect square to estimate the square root. Follow these steps:
Step 1: Write the number 78 to perform long division.
Step 2: Identify a perfect square number that is less than or equal to 78. For 78, that number is 64 (8²).
Step 3: Divide 78 by 8. The remainder will be 14, and the quotient will be 8.
Step 4: Bring down the remainder (14) and append two zeros. Add a decimal point to the quotient, making it 8.0.
Step 5: Double the quotient to use as the new divisor, which gives 16.
Step 6: Select a number that, when multiplied by the new divisor, results in a product less than or equal to 1400.
Step 7: Continue the division process to find √78 to the desired decimal places. → √78 ≈ 8.831.
In the approximation method, we estimate the square root by identifying the closest perfect squares surrounding the number.
Step 1: The nearest perfect squares to 78 are √64 = 8 and √81 = 9.
Step 2: Since 78 is between 64 and 81, we know the square root will be between 8 and 9.
Step 3: By testing numbers like 8.8, 8.9, and further, we find that √78 ≈ 8.831.
Find the square of √31.
Name any 3 irrational square root.
Find out if 25 is a perfect square.
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
: He loves to play the quiz with kids through algebra to make kids love it.