√5*√2
give me the detail answer of the question
Answers
Answer:
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Answer:
Square roots are often found in math and science problems, and any student needs to pick up the basics of square roots to tackle these questions. Square roots ask “what number, when multiplied by itself, gives the following result,” and as such working them out requires you to think about numbers in a slightly different way. However, you can easily understand the rules of square roots and answer any questions involving them, whether they require direct calculation or just simplification.
What Is a Square Root?
Square roots are the opposite of “squaring” a number, or multiplying it by itself. For example, three squared is nine (32 = 9), so the square root of nine is three. In symbols, this is √9 = 3. The “√” symbol tells you to take the square root of a number, and you can find this on most calculators.
What Is a Square Root?
Remember that every number actually has two square roots. Three multiplied by three equals nine, but negative three multiplied by negative three also equals nine, so 32 = (−3)2 = 9 and √9 = ±3, with the ± standing in for “plus or minus.” In many cases, you can ignore the negative square roots of numbers, but sometimes it’s important to remember that every number has two roots.
You may be asked to take the “cube root” or “fourth root” of a number. The cube root is the number that, when multiplied by itself twice, equals the original number. The fourth root is the number that when multiplied by itself three times equals the original number. Like square roots, these are just the opposite of taking the power of numbers. So, 33 = 27, and that means the cube root of 27 is 3, or ∛27 = 3. The “∛” symbol represents the cube root of the number that comes after it. Roots are sometimes also expressed as fractional powers, so √x = x1/2 and ∛x = x1/3.
Simplifying Square Roots
One of the most challenging tasks you may have to perform with square roots is simplifying large square roots, but you just need to follow some simple rules to tackle these questions. You can factor square roots in the same way as you factor ordinary numbers. So for example 6 = 2 × 3, so √6 = √2 × √3.
Simplifying larger roots means taking the factorization step by step and remembering the definition of a square root. For example, √132 is a big root, and it might be hard to see what to do. However, you can easily see it’s divisible by 2, so you can write √132 = √2 √66. However, 66 is also divisible by 2, so you can write: √2 √66 = √2 √2 √33. In this case, a square root of a number multiplied by another square root just gives the original number (because of the definition of square root), so √132 = √2 √2 √33 = 2 √33.
In short, you can simplify square roots using the following rules
√(a × b) = √a × √b
√a × √a = a