Question

Find the product of 30−−√ and 610−−√. Express it in standard form (i.
e., ab√). Give the value of a followed by the value of b separated by a comma.

Answer 1

the product of √30 and √610 is 10√183.


√30  = √(2×3×5)
and √610 = √(2×5×61

Since 61 can't be factorised further.
Therefore, the value of √30×√610 is
= √(2×3×5×2×5×61)
= 2×5×√(3×61)
=10√183

Answer 2

The product of $\sqrt{30}$ and $6\sqrt{10}$ in the standard form is $\boxed{60\sqrt3}$ and the value of $a$ and $b$ are $60$ and $3$ respectively.

Explanation:

The product of the number in the square root is done by factorizing the number such that the product of the two same number inside the root can be written as the single number.

The mathematical expression for the product of the two same numbers inside a root is as shown:

$\begin{aligned}\sqrt{a}.\sqrt{a}&=(\sqrt{a})^2\\&=a\end{aligned}$

Similarly, the product of the two numbers $\sqrt{30}$ and $6\sqrt{10}$ can also be taken by factorizing the number in a proper manner.

Factorize the number $\sqrt{30}$ to its simplest form.

$\begin{aligned}\sqrt{30}=\sqrt{3\times10}\\=\sqrt{3}.\sqrt{10}\end{aligned}$

The two number can now be multiplied as shown below:

$\begin{aligned}\sqrt{30}\times6\sqrt{10}&=\sqrt{3}.\sqrt{10}\times6\sqrt{10}\\&=\sqrt{3}\times(10\times6)\\&=60\sqrt{3}\end{aligned}$

Compare the value of the product to the standard form $a\sqrt{b}$.

$a\sqrt{b}=60\sqrt{3}\\a=60, b=3$

Thus, the product of $\sqrt{30}$ and $6\sqrt{10}$ in the standard form is $\boxed{60\sqrt3}$ and the value of $a$ and $b$ are $60$ and $3$ respectively.

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Answer Details:

Grade: Junior school

Subject: Physics

Chapter: Products and addition

Keywords:

product, square root, 6 root 10, root 30, standard form, values of a and b, separated, comma, followed by.