Solve the following exercise:
\( \sqrt{30}\cdot\sqrt{1}= \)
The laws of radicals are very relevant for solving exercises, and combining them with power rules can greatly help you solve exercises easily.
Solve the following exercise:
\( \sqrt{1}\cdot\sqrt{25}= \)
Solve the following exercise:
\( \sqrt{16}\cdot\sqrt{1}= \)
Solve the following exercise:
\( \sqrt{1}\cdot\sqrt{2}= \)
When the root appears across the entire product, we can break down each factor and apply the root to them, leaving the multiplication sign between the factors.
We formulate:
When the root appears over the entire quotient (over the entire fraction), we can break down each factor and apply the root to it, leaving the division sign (fraction line) between the factors.
We formulate:
Solve the following exercise:
\( \sqrt{25x^4}= \)
Choose the largest value
Solve the following exercise:
\( \sqrt{\frac{2}{4}}= \)
The root over another root, we will multiply the order of the first root by the order of the second root and the order we obtain will be executed as a root on our number. (As the rule of power over another power)
Let's put it this way:
A root is symbolized with the sign
Indeed, when we see a number with a root, we wonder what positive number raised to , will give us what is written inside the root.
A root is the opposite of a power operation. When there is no small number at the top left of the root, it denotes that it is a root of , square root.
If a small number appears on the left, this will be the order of the root.
Let's know some of the fundamental laws:
Let's see the example:
Let's ask, what power of will give us and the answer is .
True, also to the power of will give us but the result of the root must be positive!
Solve the following exercise:
\( \sqrt{5}\cdot\sqrt{5}= \)
Solve the following exercise:
\( \sqrt{2}\cdot\sqrt{5}= \)
Solve the following exercise:
\( \sqrt{3}\cdot\sqrt{3}= \)
When we find a root that is in the entirety of the product, we can break down the product's factors and leave a separate root for each of them.
We will formulate this as a rule:
Let's see this in an example:
According to the root of a product rule, we can break down the factors and leave the root of each factor separately while maintaining the multiplication operation between them:
We will break it down and obtain:
When we encounter a root that is over the entire quotient (fraction) we can break down the factors of the quotient and leave a separate root for each of them. We will place the division operation between the two factors: the fraction line.
Let's formulate it this way:
Let's see this in an example:
According to the rule of the root of a quotient, we can break down the factors and leave the root of each factor separately while maintaining the multiplication operation between them:
We will break it down and obtain:
Solve the following exercise:
\( \sqrt{10}\cdot\sqrt{3}= \)
Solve the following exercise:
\( \sqrt{5}\cdot\sqrt{6}= \)
Solve the following exercise:
\( \sqrt{2}\cdot\sqrt{2}= \)
When we encounter an exercise where there is a root over a root, we will multiply the order of the first root by the order of the second root and the order we obtain we will multiply as a root over our number. (As in the rule of power over power)
Let's formulate it this way:
Let's see this in the example:
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In the blog of Tutorela you will find a variety of articles on mathematics.
Solve the following exercise:
Let's start with a reminder of the definition of a root as a power:
We will then use the fact that raising the number 1 to any power always yields the result 1, particularly raising it to the power of half of the square root (which we obtain by using the definition of root as a power mentioned earlier),
In other words:
Therefore, the correct answer is answer C.
Solve the following exercise:
Let's start by recalling how to define a root as a power:
Next, we will remember that raising 1 to any power will always yield the result 1, even the half power of the square root.
In other words:
Therefore, the correct answer is answer D.
Solve the following exercise:
Let's start by recalling how to define a square root as a power:
Next, we remember that raising 1 to any power always gives us 1, even the half power we got from converting the square root.
In other words:
Therefore, the correct answer is answer a.
Solve the following exercise:
To simplify the given expression, we will use the following three laws of exponents:
a. Definition of root as an exponent:
b. Law of exponents for an exponent applied to terms in parentheses:
c. Law of exponents for an exponent raised to an exponent:
We'll start by converting the fourth root to an exponent using the law of exponents mentioned in a.:
We'll continue, using the law of exponents mentioned in b. and apply the exponent to each factor in the parentheses:
We'll continue, using the law of exponents mentioned in c. and perform the exponent applied to the term with an exponent in parentheses (the second factor in the multiplication):
In the final steps, we first converted the power of one-half applied to the first factor in the multiplication back to the fourth root form, again, according to the definition of root as an exponent mentioned in a. (in the reverse direction) and then calculated the known fourth root of 25.
Therefore, the correct answer is answer a.
Choose the largest value
Let's begin by calculating the numerical value of each of the roots in the given options:
We can determine that:
5>4>3>1 Therefore, the correct answer is option A
Solve the following exercise:
\( \sqrt{4}\cdot\sqrt{4}= \)
Solve the following exercise:
\( \sqrt{2}\cdot\sqrt{3}= \)
Solve the following exercise:
\( \sqrt{30}\cdot\sqrt{1}= \)