Question

multiply(4 root 5 - 3 root 2) by (3 root 5 + 5 root 2)

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

Concept:

A number y whose square (the outcome of multiplying the number by itself, or y ), is x is known as the square root of a number x in mathematics. For instance, since $4^{2} = (-4) = 16$,$4 and -4$ are the square roots of $16$.

The primary square root, also known as the nonnegative square root, of each nonnegative real number $x$ is denoted by $\sqrt{x}$  where the symbol $\sqrt{}$ is called the radical sign  or radix.

There are two square roots for any positive number x:

$\sqrt{x}$ which is positive, and $-\sqrt{x}$  which is negative. Using the sign, the two roots can be stated more succinctly as The term "the square root" is sometimes used to refer to the major square root, even though it is merely one of a positive number's two square roots.

Given:

$(4\sqrt{5} - 3\sqrt{2}) (3\sqrt{5} + 5\sqrt{2})$

Find:

To find the product of $(4\sqrt{5} - 3\sqrt{2}) (3\sqrt{5}+ 5\sqrt{2})$

Solution:

$(4 \sqrt{5} - 3 \sqrt{2}) (3\sqrt{5} + 5 \sqrt{2} )$

By opening the brackets we will get

$(4\sqrt{5} * 3\sqrt{5}) + (4\sqrt{5} * 5\sqrt{2}) - (3\sqrt{2} * 3\sqrt{5} ) - (3\sqrt{2} * 5\sqrt{2})$

⇒ $(12 * 5 ) + ( 20 \sqrt{10}) - (9\sqrt{10}) - (15 * 2)$

⇒ $60 + 20\sqrt{10} - 9\sqrt{10} - 30$

⇒ $60 - 30 + 20\sqrt{10} - 9\sqrt{10}$

⇒ $30 + 11\sqrt{10}$

Hence the solution is $30 + 11\sqrt{10}$

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