Question

Given that a*b means square root a+4b , where the positive root is taken,determine the values of 1*2

Answer 1

Given that $a \times b$ means square root a+4b Then the value of $1 \times 2 = 3$

Solution:

Given that, $a \times b$ means the square root of a + 4b , where the positive root is taken ,  

We have to determine the values of $1 \times 2$

Now, according to given information,  

$\mathrm{a} \times \mathrm{b} \rightarrow \text { square root of } \mathrm{a}+4 \mathrm{b}$

$\begin{array}{l}{\text { Then, a } \times \mathrm{b} \rightarrow \sqrt{\mathrm{a}+4 \mathrm{b}}} \\\\ {\text { Now, for } 1 \times 2, \text { we get } \mathrm{a}=1 \text { and } \mathrm{b}=2}\end{array}$

$\begin{array}{l}{\text { So, } 1 \times 2=\sqrt{1+4(2)}} \\\\ {\rightarrow 1 \times 2=\sqrt{1+8}} \\\\ {\rightarrow 1 \times 2=\sqrt{9}} \\\\ {\rightarrow 1 \times 2=\sqrt{9}} \\\\ {\rightarrow 1 \times 2=\sqrt{(\pm 3)^{2}}} \\\\ {\rightarrow 1 \times 2=\pm 3} \\\\ {\text { As we have to take only positive root. }} \\\\ {\rightarrow 1 \times 2=3}\end{array}$

Hence, the value of $1 \times 2 = 3$