Solved on Feb 04, 2024

Simplify the expression $2 \cdot 4^{\frac{1}{2}}$ to an integer or simplified fraction.

STEP 1

Assumptions
1. We need to simplify the expression $2 \cdot 4^{\frac{1}{2}}$ .
2. The exponent $\frac{1}{2}$ represents the square root.

STEP 2

Understand the meaning of the exponent $\frac{1}{2}$ . It indicates that we need to find the square root of the base number.
$a^{\frac{1}{2}} = \sqrt{a}$

STEP 3

Apply the exponent rule to the base number 4.
$4^{\frac{1}{2}} = \sqrt{4}$

STEP 4

Calculate the square root of 4.
$\sqrt{4} = 2$

STEP 5

Now, multiply the result by 2 as indicated by the original expression.
$2 \cdot 4^{\frac{1}{2}} = 2 \cdot 2$

STEP 6

Calculate the product.
$2 \cdot 2 = 4$
The expression $2 \cdot 4^{\frac{1}{2}}$ simplifies to the integer 4.

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Simplify the expression $2 \cdot 4^{\frac{1}{2}}$ to an integer or simplified fraction.

STEP 1

Assumptions
1. We need to simplify the expression $2 \cdot 4^{\frac{1}{2}}$ .
2. The exponent $\frac{1}{2}$ represents the square root.

STEP 2

Understand the meaning of the exponent $\frac{1}{2}$ . It indicates that we need to find the square root of the base number.
$a^{\frac{1}{2}} = \sqrt{a}$

STEP 3

Apply the exponent rule to the base number 4.
$4^{\frac{1}{2}} = \sqrt{4}$

STEP 4

Calculate the square root of 4.
$\sqrt{4} = 2$

STEP 5

Now, multiply the result by 2 as indicated by the original expression.
$2 \cdot 4^{\frac{1}{2}} = 2 \cdot 2$

STEP 6

Calculate the product.
$2 \cdot 2 = 4$
The expression $2 \cdot 4^{\frac{1}{2}}$ simplifies to the integer 4.

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Simplify the expression 2⋅4122 \cdot 4^{\frac{1}{2}}2⋅421​ to an integer or simplified fraction.

STEP 1

Assumptions1. We need to simplify the expression 2⋅4122 \cdot 4^{\frac{1}{2}}2⋅421​.2. The exponent 12\frac{1}{2}21​ represents the square root.

STEP 2

Understand the meaning of the exponent 12\frac{1}{2}21​. It indicates that we need to find the square root of the base number.a12=aa^{\frac{1}{2}} = \sqrt{a}a21​=a​

STEP 3

Apply the exponent rule to the base number 4.412=44^{\frac{1}{2}} = \sqrt{4}421​=4​

STEP 4

Calculate the square root of 4.4=2\sqrt{4} = 24​=2

STEP 5

Now, multiply the result by 2 as indicated by the original expression.2⋅412=2⋅22 \cdot 4^{\frac{1}{2}} = 2 \cdot 22⋅421​=2⋅2

STEP 6

Calculate the product.2⋅2=42 \cdot 2 = 42⋅2=4The expression 2⋅4122 \cdot 4^{\frac{1}{2}}2⋅421​ simplifies to the integer 4.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Simplify the expression $2 \cdot 4^{\frac{1}{2}}$ to an integer or simplified fraction.

Assumptions
1. We need to simplify the expression $2 \cdot 4^{\frac{1}{2}}$ .
2. The exponent $\frac{1}{2}$ represents the square root.

Understand the meaning of the exponent $\frac{1}{2}$ . It indicates that we need to find the square root of the base number.
$a^{\frac{1}{2}} = \sqrt{a}$

Apply the exponent rule to the base number 4.
$4^{\frac{1}{2}} = \sqrt{4}$

Calculate the square root of 4.
$\sqrt{4} = 2$

Now, multiply the result by 2 as indicated by the original expression.
$2 \cdot 4^{\frac{1}{2}} = 2 \cdot 2$

Calculate the product.
$2 \cdot 2 = 4$
The expression $2 \cdot 4^{\frac{1}{2}}$ simplifies to the integer 4.