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How do you simplify $3\sqrt {50} \cdot \sqrt {22} ?$?

Last updated date: 13th Jun 2024
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Hint: As we know that square root can be defined as a number which when multiplied by itself gives a number as the product. For example$5*5 = 25$, here square root of $25$is $5$. There is no such formula to calculate square root formula but two ways are generally considered. They are the prime factorization method and division method. The symbol $\sqrt {} $ is used to denote square roots and this symbol of square roots is also known as radical.

Complete step by step solution:
Here we have $3\sqrt {50} \cdot \sqrt {22} $, since both are non perfect squares so we will
factorise it under the root: $3\sqrt {25 \cdot 2} \times \sqrt {22} $, $50$ can be written as $25
\times 2$ and we know that $25$ is a perfect square and we can take 5 out of the radical so we get,
$3 \times 5\sqrt 2 \times \sqrt {22} $$ = 15\sqrt 2 \times \sqrt {22} $.
It can be further written as $15\sqrt {2 \times 22} \Rightarrow 15\sqrt {44} $,Here $44$can be written as $4*11$ and we know that $4$, so $2$ can be taken out. It gives $15 \times *\sqrt {4*11}
\Rightarrow 15*2\sqrt {11} $. So we get $30\sqrt {11} $.
Hence the answer is $30\sqrt {11} $.

Note: The above given numbers are non-perfect squares as we know that a non-perfect square is a number that there is no rational number i.e. it is considered as an irrational number.
Their decimal does not end and they do not repeat a pattern so they are also non-terminating and non- repeating numbers. The number written inside the square root symbol or radical is known as radicand. We know that all real numbers have two square roots, one is a positive square root and another one is a negative square root. The positive square root is also referred to as the principal square root.