Is the square root of 7 a real number?
Understand the Problem
The question is asking whether the square root of 7 is a real number. This involves understanding the properties of square roots and real numbers in mathematics.
Answer
Yes, the square root of 7 is a real number, $\sqrt{7}$.
Answer for screen readers
Yes, the square root of 7 is a real number, expressed as $\sqrt{7}$.
Steps to Solve
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Definition of Square Roots The square root of a number $x$ is defined as a value $y$ such that when $y$ is multiplied by itself, it results in $x$. Mathematically, this is represented as: $$ y^2 = x $$
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Determine the Square Root of 7 We need to find a number $y$ such that: $$ y^2 = 7 $$
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Determining if the Square Root is Real Since 7 is a positive number, its square root can be expressed as: $$ y = \sqrt{7} $$ The square root of any positive number is always a real number.
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Conclusion Since $7 > 0$, we conclude that $\sqrt{7}$ is indeed a real number.
Yes, the square root of 7 is a real number, expressed as $\sqrt{7}$.
More Information
The square root of 7 is an irrational number, approximately equal to 2.6457513110645906. This means it cannot be expressed as a fraction of two integers, and its decimal representation is non-repeating and non-terminating.
Tips
Common mistakes include assuming that the square root of a number must always be an integer or overlooking that positive numbers can yield real square roots.
