is the square root of 0 9 irrational

is the square root of 0 9 irrational Square root of 25 25 5 since 5 5 25 Square root of 36 36 6 since 6 6 36 Square root of 49 49 7 since 7 7 49 Square root of 64 64 8 since 8 8 64 Square root of 81 81 9 since 9 9 81 Square root of 100 100 10 since 10 10 100

An irrational number is a real number that cannot be expressed as a ratio of integers for example 2 is an irrational number We cannot express any irrational number in the form of a ratio such as p q where p and q are integers q 0 Again the decimal expansion of an irrational number is neither terminating nor recurring Read more If we can write a number as a fraction that has both an integer numerator and an integer denominator then it is rational If we can t then it is irrational Repeating decimals are rational because we can write them as fractions For example if we take 0 7

is the square root of 0 9 irrational

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The negative solution of x2 a is a we know that if x satisfies x2 a then x 2 x2 a therefore because a is a solution so is a So for a 0 a 0 but there are two solutions to the equation x2 a one positive a and one negative a FORMULA Let our first irrational number be a x a x where a a is the rational and x x the irrational parts Let the other irrational number be b x b x where b b is the rational and x x the irrational parts Then a x b x a b x a x b x a b x Example 3 89

The principal root of 9 is 3 so it s 3 times the square root of 5 So this is going to be 9 plus 3 times the square root of 5 So the square root of 5 is irrational Square root of 2 irrational number Phi the golden ratio irrational number So these things that really just pop out of nature many of these numbers are irrational

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Let s think about square roots now Square roots of perfect squares are always whole numbers so they are rational But the decimal forms of square roots of numbers that are not perfect squares never stop and The square root of a number can be a rational or irrational number depending on the condition and the number If the square root is a perfect square then it would be a rational number On the other side if the square root of the number is not perfect it will be an irrational number i e 10 3 16227766017 Examples References

Explanation The square root is an irrational number so you won t be able to get an exact answer for that But I guess you can simplify it instead 0 9 9 0 1 3 0 1 Or if you want a more exact answer you can use a calculator to get an approximate square root 0 9 0 94868329805 Answer link Proof Suppose not The square root of any irrational number is rational Let m m be some irrational number It follows that m m is rational By definition of a rational number there are two positive integers p p and q q such that m q p m q p m q2 p2 m q 2 p 2

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is the square root of 0 9 irrational - The negative solution of x2 a is a we know that if x satisfies x2 a then x 2 x2 a therefore because a is a solution so is a So for a 0 a 0 but there are two solutions to the equation x2 a one positive a and one negative a