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 * b` means square root a+4b Then the value of
`1 * 2 = 3`

Solution:

Given that,
`a * b` means the square root of a + 4b , where the positive root is taken ,

We have to determine the values of
`1 * 2`

Now, according to given information,

`\mathrm{a} * \mathrm{b} \rightarrow \text { square root of } \mathrm{a}+4 \mathrm{b}`

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

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

Hence, the value of
`1 * 2 = 3`