If
$\text{\hspace{0.17em}}a\text{\hspace{0.17em}}$ and
$\text{\hspace{0.17em}}b\text{\hspace{0.17em}}$ are nonnegative, the square root of the product
$\text{\hspace{0.17em}}ab\text{\hspace{0.17em}}$ is equal to the product of the square roots of
$\text{\hspace{0.17em}}a\text{\hspace{0.17em}}$ and
$\text{\hspace{0.17em}}b.\text{\hspace{0.17em}}$
$\sqrt{ab}=\sqrt{a}\cdot \sqrt{b}$
Given a square root radical expression, use the product rule to simplify it.
Factor any perfect squares from the radicand.
Write the radical expression as a product of radical expressions.
$5\left|x\right|\left|y\right|\sqrt{2yz}.\text{\hspace{0.17em}}$ Notice the absolute value signs around
x and
y ? That’s because their value must be positive!
Just as we can rewrite the square root of a product as a product of square roots, so too can we rewrite the square root of a quotient as a quotient of square roots, using the
quotient rule for simplifying square roots. It can be helpful to separate the numerator and denominator of a fraction under a radical so that we can take their square roots separately. We can rewrite
$\text{\hspace{0.17em}}\sqrt{\frac{5}{2}}\text{\hspace{0.17em}}$ as
$\text{\hspace{0.17em}}\frac{\sqrt{5}}{\sqrt{2}}.$
The quotient rule for simplifying square roots
The square root of the quotient
$\text{\hspace{0.17em}}\frac{a}{b}\text{\hspace{0.17em}}$ is equal to the quotient of the square roots of
$\text{\hspace{0.17em}}a\text{\hspace{0.17em}}$ and
$\text{\hspace{0.17em}}b,$ where
$\text{\hspace{0.17em}}b\ne 0.$
$\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$
Given a radical expression, use the quotient rule to simplify it.
Write the radical expression as the quotient of two radical expressions.
$\frac{x\sqrt{2}}{3{y}^{2}}.\text{\hspace{0.17em}}$ We do not need the absolute value signs for
$\text{\hspace{0.17em}}{y}^{2}\text{\hspace{0.17em}}$ because that term will always be nonnegative.
We can add or subtract radical expressions only when they have the same radicand and when they have the same radical type such as square roots. For example, the sum of
$\text{\hspace{0.17em}}\sqrt{2}\text{\hspace{0.17em}}$ and
$\text{\hspace{0.17em}}3\sqrt{2}\text{\hspace{0.17em}}$ is
$\text{\hspace{0.17em}}4\sqrt{2}.\text{\hspace{0.17em}}$ However, it is often possible to simplify radical expressions, and that may change the radicand. The radical expression
$\text{\hspace{0.17em}}\sqrt{18}\text{\hspace{0.17em}}$ can be written with a
$\text{\hspace{0.17em}}2\text{\hspace{0.17em}}$ in the radicand, as
$\text{\hspace{0.17em}}3\sqrt{2},$ so
$\text{\hspace{0.17em}}\sqrt{2}+\sqrt{18}=\sqrt{2}+3\sqrt{2}=4\sqrt{2}.$
Given a radical expression requiring addition or subtraction of square roots, solve.
An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table.
Carole
I'm 13 and I understand it great
AJ
I am 1 year old but I can do it! 1+1=2 proof very hard for me though.
Atone
hi
Adu
Not really they are just easy concepts which can be understood if you have great basics. I am 14 I understood them easily.
Vedant
find the 15th term of the geometric sequince whose first is 18 and last term of 387