Chapter 9.8, Problem 47MR

To determine

The expression in simplified form.

Answer to Problem 47MR

  $\sqrt{1.44}=1.2$

Explanation of Solution

Given:

The given expression is:

  $\sqrt{1.44}$

Calculation:

The given expression can be written as a fraction as:

  $\sqrt{\frac{1.44}{1}}$

Solve further;

  $\begin{array}{l}\sqrt{1.44}=\sqrt{\frac{1.44}{1}}\\ \sqrt{1.44}=\sqrt{\frac{144}{100}}\end{array}$

According to the law of indices, for any real number, say, a and b where b is not equal to 0;

  $\begin{array}{l}\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}\\ \therefore \\ \sqrt{\frac{144}{100}}=\frac{\sqrt{144}}{\sqrt{100}}\end{array}$

According to the law of indices, for any real number, say, a:

  $\sqrt{a}=a^{\frac{1}{2}}$

Therefore, the given expression can be simplified as:

  $\begin{array}{l}\sqrt{\frac{144}{100}}=\frac{\sqrt{144}}{\sqrt{100}}\\ \sqrt{\frac{144}{100}}=\frac{{\left(144\right)}^{\frac{1}{2}}}{{\left(100\right)}^{\frac{1}{2}}}\\ \sqrt{\frac{144}{100}}=\frac{{\left({12}^2\right)}^{\frac{1}{2}}}{{\left({10}^2\right)}^{\frac{1}{2}}}\end{array}$

It is known from the law of indices that for any real numbers a, m and n;

  ${\left(a^m\right)}^n=a^{m\times n}$

Hence,

  $\begin{array}{l}\sqrt{\frac{144}{100}}=\frac{{\left({12}^2\right)}^{\frac{1}{2}}}{{\left({10}^2\right)}^{\frac{1}{2}}}\\ \sqrt{\frac{144}{100}}=\frac{{12}^{2\times }{}^{\frac{1}{2}}}{{10}^{2\times }{}^{\frac{1}{2}}}\\ \sqrt{\frac{144}{100}}=\frac{{12}^1}{{10}^1}\\ \sqrt{\frac{144}{100}}=\frac{12}{10}\end{array}$

Express the final result in decimal:

  $\begin{array}{l}\sqrt{\frac{144}{100}}=\frac{12}{10}\\ \sqrt{1.44}=1.2\end{array}$