Answer

Verified

373.5k+ views

**Hint:**To solve this question, first we will try to observe the given expression by removing the negative sign from the expression, and then we will discuss the term how $\sqrt { - 1} $ is related to $i$. And finally, simplify the positive square root expression to get the final answer.

**Complete step by step solution:**

The given special symbol, $i$, is used to represent the square root of negative 1, $\sqrt { - 1} $.

As we know, there is no such thing in the real number universe as the $\sqrt { - 1} $ because there are no two identical numbers that we can multiply together to get -1 as the exact solution.

$1.1 = 1$ and $ - 1. - 1$ is also 1. Obviously $1. - 1 = - 1$ , but 1 and -1 are not the same number. They both have the same magnitude(distance from zero), but they are not identical.

So, when we have a number that involves a negative square root, math developed a plan to get around that problem by saying that anytime we run across that issue, we make our number positive so we can deal with it and put an $i$ at the end.

So, in this case:

$

\sqrt { - 45} \\

= \sqrt {45} \times \sqrt { - 1} \\

\\

$

As $i = \sqrt { - 1} $ :

$\therefore \sqrt { - 45} = \sqrt {45} i$

Since, $45 = 9 \times 5$ , the answer can be simplified to:

$\because \sqrt {45} i = \sqrt {9.5} i = 3\sqrt 5 i$

**Hence, the given expression in terms of $i$ is $3\sqrt 5 i$.**

**Note:**

Iota, $i$, is a Greek letter that is widely used in mathematics to denote the imaginary part of a complex number. Let's say we have an equation: ${x^2} + 1 = 0$ . In this case, the value of $x$ will be the square root of -1, which is fundamentally not possible.

Recently Updated Pages

The base of a right prism is a pentagon whose sides class 10 maths CBSE

A die is thrown Find the probability that the number class 10 maths CBSE

A mans age is six times the age of his son In six years class 10 maths CBSE

A started a business with Rs 21000 and is joined afterwards class 10 maths CBSE

Aasifbhai bought a refrigerator at Rs 10000 After some class 10 maths CBSE

Give a brief history of the mathematician Pythagoras class 10 maths CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Name 10 Living and Non living things class 9 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE

Write the 6 fundamental rights of India and explain in detail