QuestionSimplify $\sqrt{49 m^{5} j^{6}}$ .

Studdy Solution

STEP 1

Assumptions1. We are asked to simplify the expression $\sqrt{49 m^{5} j^{6}}$ . . The expression is a square root, which means we are looking for the product of two identical factors that will give us the expression under the square root.
3. The laws of exponents apply, which means that when we take the square root of a variable raised to an exponent, we divide the exponent by.

STEP 2

First, let's simplify the square root of the constant,49.
$\sqrt{49}$

STEP 3

Calculate the square root of49.
$\sqrt{49} =7$

STEP 4

Next, let's simplify the square root of $m^{}$ . Since is an odd number, we can't directly take the square root. However, we can express as4 +1, which allows us to simplify the expression.
$\sqrt{m^{}} = \sqrt{m^{4} \cdot m^{1}}$

STEP 5

Now, we can take the square root of $m^{4}$ and $m^{1}$ separately.
$\sqrt{m^{4} \cdot m^{1}} = \sqrt{m^{4}} \cdot \sqrt{m^{1}}$

STEP 6

Calculate the square root of $m^{4}$ and $m^{1}$ .
$\sqrt{m^{4}} \cdot \sqrt{m^{1}} = m^{2} \cdot m$

STEP 7

Next, let's simplify the square root of $j^{6}$ . Since6 is an even number, we can directly take the square root.
$\sqrt{j^{6}}$

STEP 8

Calculate the square root of $j^{6}$ .
$\sqrt{j^{6}} = j^{3}$

STEP 9

Now, we can combine all the simplified parts to get the simplified form of the original expression.
$\sqrt{49 m^{5} j^{6}} =7 \cdot m^{2} \cdot m \cdot j^{3}$

STEP 10

Finally, we can simplify the expression further by combining the $m$ terms.
$7 \cdot m^{2} \cdot m \cdot j^{3} =7m^{3}j^{3}$ The simplified form of $\sqrt{49 m^{5} j^{6}}$ is $7m^{3}j^{3}$ .

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QuestionSimplify $\sqrt{49 m^{5} j^{6}}$ .

Studdy Solution

STEP 1

STEP 2

First, let's simplify the square root of the constant,49.
$\sqrt{49}$

STEP 3

Calculate the square root of49.
$\sqrt{49} =7$

STEP 4

Next, let's simplify the square root of $m^{}$ . Since is an odd number, we can't directly take the square root. However, we can express as4 +1, which allows us to simplify the expression.
$\sqrt{m^{}} = \sqrt{m^{4} \cdot m^{1}}$

STEP 5

Now, we can take the square root of $m^{4}$ and $m^{1}$ separately.
$\sqrt{m^{4} \cdot m^{1}} = \sqrt{m^{4}} \cdot \sqrt{m^{1}}$

STEP 6

Calculate the square root of $m^{4}$ and $m^{1}$ .
$\sqrt{m^{4}} \cdot \sqrt{m^{1}} = m^{2} \cdot m$

STEP 7

Next, let's simplify the square root of $j^{6}$ . Since6 is an even number, we can directly take the square root.
$\sqrt{j^{6}}$

STEP 8

Calculate the square root of $j^{6}$ .
$\sqrt{j^{6}} = j^{3}$

STEP 9

Now, we can combine all the simplified parts to get the simplified form of the original expression.
$\sqrt{49 m^{5} j^{6}} =7 \cdot m^{2} \cdot m \cdot j^{3}$

STEP 10

Finally, we can simplify the expression further by combining the $m$ terms.
$7 \cdot m^{2} \cdot m \cdot j^{3} =7m^{3}j^{3}$ The simplified form of $\sqrt{49 m^{5} j^{6}}$ is $7m^{3}j^{3}$ .

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QuestionSimplify 49m5j6\sqrt{49 m^{5} j^{6}}49m5j6​.

Studdy Solution

STEP 1

STEP 2

First, let's simplify the square root of the constant,49.49\sqrt{49}49​

STEP 3

Calculate the square root of49.49=7\sqrt{49} =749​=7

STEP 4

Next, let's simplify the square root of mm^{}m. Since is an odd number, we can't directly take the square root. However, we can express as4 +1, which allows us to simplify the expression.m=m4⋅m1\sqrt{m^{}} = \sqrt{m^{4} \cdot m^{1}}m​=m4⋅m1​

STEP 5

Now, we can take the square root of m4m^{4}m4 and m1m^{1}m1 separately.m4⋅m1=m4⋅m1\sqrt{m^{4} \cdot m^{1}} = \sqrt{m^{4}} \cdot \sqrt{m^{1}}m4⋅m1​=m4​⋅m1​

STEP 6

Calculate the square root of m4m^{4}m4 and m1m^{1}m1.m4⋅m1=m2⋅m\sqrt{m^{4}} \cdot \sqrt{m^{1}} = m^{2} \cdot mm4​⋅m1​=m2⋅m

STEP 7

Next, let's simplify the square root of j6j^{6}j6. Since6 is an even number, we can directly take the square root.j6\sqrt{j^{6}}j6​

STEP 8

Calculate the square root of j6j^{6}j6.j6=j3\sqrt{j^{6}} = j^{3}j6​=j3

STEP 9

Now, we can combine all the simplified parts to get the simplified form of the original expression.49m5j6=7⋅m2⋅m⋅j3\sqrt{49 m^{5} j^{6}} =7 \cdot m^{2} \cdot m \cdot j^{3}49m5j6​=7⋅m2⋅m⋅j3

STEP 10

Finally, we can simplify the expression further by combining the mmm terms.7⋅m2⋅m⋅j3=7m3j37 \cdot m^{2} \cdot m \cdot j^{3} =7m^{3}j^{3}7⋅m2⋅m⋅j3=7m3j3The simplified form of 49m5j6\sqrt{49 m^{5} j^{6}}49m5j6​ is 7m3j37m^{3}j^{3}7m3j3.

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QuestionSimplify $\sqrt{49 m^{5} j^{6}}$ .

First, let's simplify the square root of the constant,49.
$\sqrt{49}$

Calculate the square root of49.
$\sqrt{49} =7$

Next, let's simplify the square root of $m^{}$ . Since is an odd number, we can't directly take the square root. However, we can express as4 +1, which allows us to simplify the expression.
$\sqrt{m^{}} = \sqrt{m^{4} \cdot m^{1}}$

Now, we can take the square root of $m^{4}$ and $m^{1}$ separately.
$\sqrt{m^{4} \cdot m^{1}} = \sqrt{m^{4}} \cdot \sqrt{m^{1}}$

Calculate the square root of $m^{4}$ and $m^{1}$ .
$\sqrt{m^{4}} \cdot \sqrt{m^{1}} = m^{2} \cdot m$

Next, let's simplify the square root of $j^{6}$ . Since6 is an even number, we can directly take the square root.
$\sqrt{j^{6}}$

Calculate the square root of $j^{6}$ .
$\sqrt{j^{6}} = j^{3}$

Now, we can combine all the simplified parts to get the simplified form of the original expression.
$\sqrt{49 m^{5} j^{6}} =7 \cdot m^{2} \cdot m \cdot j^{3}$

Finally, we can simplify the expression further by combining the $m$ terms.
$7 \cdot m^{2} \cdot m \cdot j^{3} =7m^{3}j^{3}$ The simplified form of $\sqrt{49 m^{5} j^{6}}$ is $7m^{3}j^{3}$ .