Question

Mai's younger brother tells her that 10/7 is equal to square root of 2. Mai knows this can't be right,
because 10/7 is rational and square root of 2 is irrational. Write an explanation that Mai could use
to convince her brother that 10/7 cannot be the square root of 2.
​

Answer 1

Answer:

10/7 is a simple fraction, and √2 cannot be written as a simple fraction. So, they are not the same.

Step-by-step explanation:

10/7 is a number that has a numerator and a denominator.

Suppose √2 = 10/7, then √2 can also be written as a number that has a numerator and a denominator.

Since this is not the case, 10/7 cannot be the same as √2.

Answer 2

10/7 is not equal to √2 because √2 cannot be defined in the form of $\dfrac{p}{q}$.

Important information:

• According to Mai's younger brother $\dfrac{10}{7}=\sqrt{2}$.

Rational and irrational numbers:

A rational number can be defined in the form of $\dfrac{p}{q}$, where p and q are integers and q is non zero.

The number $\dfrac{10}{7}$ is a rational number.

The number $\sqrt{2}$ cannot be defined in the form of $\dfrac{p}{q}$, so it is an irrational number.

We know that a rational and an irrational number cannot be equal to each other.

Therefore, $\dfrac{10}{7}\neq \sqrt{2}$.

Find out more about 'Rational and irrational numbers' here:

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