Tag: square and square root

Questions Related to square and square root

Which one of the following statements is correct?

maths square and square root scientific notation use of exponents power of 10

  1. There can be a real number which is both rational and irrational.

  2. The sum of two irrational numbers is always irrational.

  3. For any real numbers x and y, $x < y \Rightarrow x^{2} < y^{2}$

  4. Every integer is a rational number.

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Correct Option: D
Explanation:

Every integer can be expressed as a rational number by dividing itself by 1.
Now, it becomes a rational number with the numerator the number itself and denominator 1.

The $p/q$ form of $0.5\bar {6}$ is 

maths square and square root scientific notation use of exponents power of 10

  1. $56/100$

  2. $56/99$

  3. $59/90$

  4. $51/90$

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Correct Option: D
Explanation:

$\begin{array}{l} x=0.566\ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _  \ 10x=5.666\ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ (i) \ 100x=56.6666\ _ \ _ \ _ \ _ \ _ \ _ (ii) \ (ii)-(i) \ 90x=51 \ x=\frac { { 51 } }{ { 90 } }  \end{array}$

If the decimal number $\displaystyle 2^{111}$ is written in the octal system then what is its unit place digit?

maths square and square root scientific notation use of exponents power of 10

  1. $0$

  2. $1$

  3. $2$

  4. $3$

Show answer
Correct Option: A
Explanation:

Here,$ 2^{111}$ = $2^{3\times27}$
which is divisible by $2^{3} = 8$
Hence, the digit in the unit place is 0