why is 1 root 2 the same as root 2 2

why is 1 root 2 the same as root 2 2 The number frac 1 sqrt 2 is defined to be the number such that when you multiply it by sqrt 2 you get 1 Symbolically it is the solution to x cdot sqrt 2 1 That s how

left frac sqrt2 1 right left frac sqrt2 sqrt2 right frac 2 sqrt2 This happens clearly because the two square roots cancel each other out due to the fact that the squaring operator Sqrt 2 Sqrt 2 Sqrt 2 Now multiplying roots by each other yields a square root of the multiplication product of the numbers under the root So Sqrt 2 Sqrt 2 Sqrt 4 which equals 2

why is 1 root 2 the same as root 2 2

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why is 1 root 2 the same as root 2 2
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Solved Which Of The Following Is Equivalent To 7 Square Root 2 3
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What is the difference between two equal roots and two different roots If you have two different roots then the parabola intersects the OX axis at two different points In The square root of a number a a denoted sqrt a a is the number b b such that b 2 a text and b ge 0 b2 a and b 0 The square root symbol sqrt is also sometimes called a radical The number or expression underneath the

1 Sqrt 2 Sqrt 2 Sqrt 2 yields Sqrt 2 Sqrt 2 Sqrt 2 Now multiplying roots by each other yields a square root of the multiplication product of the numbers under the root So Sqrt 2 Roots are nice but we prefer dealing with regular numbers as much as possible So for example instead of 4 we prefer dealing with 2 What about roots that aren t equal to an integer like

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We have defined x frac 1 2 to mean sqrt x because is the only choice that fits the different rules for exponentials you learn like x a cdot x b x a b or x a b x ab There are two square roots but the symbol means just the principal square root Example The square roots of 36 are 6 and 6 But 36 6 not 6 The Principal Square Root is sometimes called the Positive Square Root but it

The square root of 2 approximately 1 4142 is the positive real number that when multiplied by itself or squared equals the number 2 It may be written in mathematics as or It is an Explanation 1 2 2 2 1 1 2 2 2 2 2

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why is 1 root 2 the same as root 2 2 - Divide both sides by 2 and displaystyle c 2 to get displaystyle frac s 2 c 2 frac 1 2 Taking the positive square root of both sides gives displaystyle