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Suppose sqrt(2) < 1 and assume that only the positive sqrt is being considered.
Then square both sides of the inequality: 2 < 1 which is a contradiction.
So the supposition is wrong ie sqrt(2) > 1
Of course, there is a sqrt of 2 which is not >1, and that is -1.4142..
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When is a square root less than the number?
when the number is greater than 1
Can The square root of a number be greater than that number?
Yes, if the number is less than 1
What happens when you repeatedly calculate the square root of anumber that is greater than one?
You eventually get the answer 1
The square root of a number is x is always less than x?
only if x is greater than 1
1 is what than the square root of 2?
1 is less than the square root of 2.
Is the square root of a number greater than the square of the number?
Yes, if the number is less than '1'.Just the opposite, if the number is greater than '1'.
When is a square root less than the number?
when the number is greater than 1
True or false- a square number is always bigger than it's square root?
False. Only a square number greater than 1 is always bigger than its root. For example, the root of 16 is 4, but the root of 1/16 (0.0625) is 1/4 (0.25) and the square root of 1 is 1.
Is five and one fourth greater than less than or equals square root twenty six?
5 1/4 = 5.25 square root of 26 approximately equal to 5.099 Hence 5.25 > 5.099 or 5 1/4 is greater than square root of 26
Can The square root of a number be greater than that number?
Yes, if the number is less than 1
What happens when you repeatedly calculate the square root of anumber that is greater than one?
You eventually get the answer 1
The square root of a number is x is always less than x?
only if x is greater than 1
The square root of a number x is always less than x?
No. The square roots of numbers between 0 and 1 (not including 0) are greater than or equal to (in the case of 1) the number. The square root of 0.49 is 0.7 for example.
1 is what than the square root of 2?
1 is less than the square root of 2.
What is an irrational number greater than 1 but less than 2?
The square root of 2 and the square root of 3 both qualify. Both of these are irrational and both are greater than 1 but less than 2. There are, of course, uncountably infinite different irrational numbers in the range between 1 and 2 and countably infinite rational numbers.
Is the square root of a number always bigger than its square root?
No, not always since: if a number is more than 1, then its square root is smaller than the number. if a number is less than 1, then its square root is bigger than the number.
When is the Square root of x greater than x?
when x is a negative number --- is a wrong answer since square root of a negative number is not defined. So x has to be zero or a positive number. The correct answer is that when x lies between 0 and 1 (with both limits excluded), its square root is greater than the number itself. Of course at both limits, the square root (assuming the positive square root - since a square root of a number can be positive or negative, both with the same absolute value) is the same as the number.
