Chapter 9.1, Problem 4PSA

a

To determine

To simplify: The Value of $4\sqrt{3}+7\sqrt{3}$

Answer to Problem 4PSA

The Values of expression is $11\sqrt{3}$ .

Explanation of Solution

Given information :

The following expression is given:$4\sqrt{3}+7\sqrt{3}$

Calculation: $4\sqrt{3}+7\sqrt{3}$

  $\begin{array}{l}\Rightarrow (4+7)\sqrt{3}\\ \Rightarrow 11\sqrt{3}\end{array}$

b

To determine

To simplify: The Value of given expression i.e. $7\sqrt{2}+\sqrt{3}+6\sqrt{3}+\sqrt{2}$

Answer to Problem 4PSA

The Values of expression is $8\sqrt{2}+7\sqrt{3}$ .

Explanation of Solution

Given information :

The following expression is given:

  $7\sqrt{2}+\sqrt{3}+6\sqrt{3}+\sqrt{2}$

Calculation:$7\sqrt{2}+\sqrt{3}+6\sqrt{3}+\sqrt{2}$

  $\begin{array}{l}\Rightarrow 7\sqrt{2}+\sqrt{2}+\sqrt{3}+6\sqrt{3}\\ \Rightarrow (7+1)\sqrt{2}+(1+6)\sqrt{3}\\ \Rightarrow 8\sqrt{2}+7\sqrt{3}\end{array}$

c

To determine

To simplify: The Value of $\sqrt{12}+\sqrt{27}$ .

Answer to Problem 4PSA

The Values of expression is $5\sqrt{3}$ .

Explanation of Solution

Given information :

The following expression is given:$\sqrt{12}+\sqrt{27}$

Calculation: $\sqrt{12}+\sqrt{27}$

  $\begin{array}{l}\Rightarrow \sqrt{3\times 4}+\sqrt{3\times 9}\\ \Rightarrow \sqrt{3}\times \sqrt{4}+\sqrt{3}\times \sqrt{9}\\ \Rightarrow \sqrt{3}\times 2+\sqrt{3}\times 3\\ \Rightarrow 2\sqrt{3}+3\sqrt{3}\\ \Rightarrow (2+3)\sqrt{3}\\ \Rightarrow 5\sqrt{3}\end{array}$

d

To determine

To simplify: The Value of $\sqrt{72}+\sqrt{75}-\sqrt{48}$

Answer to Problem 4PSA

The Values of expression is $6\sqrt{2}+\sqrt{3}$ .

Explanation of Solution

Given information :

The following expression is given:$\sqrt{72}+\sqrt{75}-\sqrt{48}$

Calculation:$\sqrt{72}+\sqrt{75}-\sqrt{48}$

  $\begin{array}{l}\Rightarrow \sqrt{2\times 36}+\sqrt{3\times 25}-\sqrt{3\times 16}\\ \Rightarrow \sqrt{2}\times \sqrt{36}+\sqrt{3}\times \sqrt{25}-\sqrt{3}\times \sqrt{16}\\ \Rightarrow \sqrt{2}\times 6+\sqrt{3}\times 5-\sqrt{3}\times 4\\ \Rightarrow 6\sqrt{2}+5\sqrt{3}-4\sqrt{3}\\ \Rightarrow 6\sqrt{2}+(5-4)\sqrt{3}\\ \Rightarrow 6\sqrt{2}+\sqrt{3}\end{array}$