QuestionWhich pair are like radicals? 1) $\sqrt[4]{5}$ and $\sqrt[4]{5}$ 2) $3 \sqrt{x}$ and $\sqrt{3 x}$ 3) $35 \sqrt{5}$ and $y \sqrt{5}$ 4) $3 \sqrt[9]{x}$ and $5 \sqrt[3]{y}$

Studdy Solution

STEP 1

Assumptions1. Like radicals are radicals that have the same index and the same radicand. The index is the root number (such as the in a square root, or the3 in a cube root), and the radicand is the number under the root symbol.

STEP 2

Now, let's examine each pair to see if they are like radicals.
The first pair is $\sqrt[4]{5}$ and $\sqrt[4]{5}$ . These are like radicals because they have the same index (4) and the same radicand (5).

STEP 3

The second pair is $3 \sqrt{x}$ and $\sqrt{3 x}$ . These are not like radicals because the radicands are different ( $x$ vs $3x$ ).

STEP 4

The third pair is $35 \sqrt{}$ and $y \sqrt{}$ . These are like radicals because they have the same index (which is2, implied for square roots) and the same radicand (). Note that the coefficients (35 and y) do not affect whether they are like radicals.

STEP 5

The fourth pair is $3 \sqrt[9]{x}$ and $5 \sqrt[3]{y}$ . These are not like radicals because both the indices (9 vs3) and the radicands ( $x$ vs $y$ ) are different.

STEP 6

Therefore, the pairs that consist of like radicals are $\sqrt[4]{5}$ and $\sqrt[4]{5}$ , and $35 \sqrt{5}$ and $y \sqrt{5}$ .

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QuestionWhich pair are like radicals? 1) $\sqrt[4]{5}$ and $\sqrt[4]{5}$ 2) $3 \sqrt{x}$ and $\sqrt{3 x}$ 3) $35 \sqrt{5}$ and $y \sqrt{5}$ 4) $3 \sqrt[9]{x}$ and $5 \sqrt[3]{y}$

Studdy Solution

STEP 1

Assumptions1. Like radicals are radicals that have the same index and the same radicand. The index is the root number (such as the in a square root, or the3 in a cube root), and the radicand is the number under the root symbol.

STEP 2

Now, let's examine each pair to see if they are like radicals.
The first pair is $\sqrt[4]{5}$ and $\sqrt[4]{5}$ . These are like radicals because they have the same index (4) and the same radicand (5).

STEP 3

The second pair is $3 \sqrt{x}$ and $\sqrt{3 x}$ . These are not like radicals because the radicands are different ( $x$ vs $3x$ ).

STEP 4

The third pair is $35 \sqrt{}$ and $y \sqrt{}$ . These are like radicals because they have the same index (which is2, implied for square roots) and the same radicand (). Note that the coefficients (35 and y) do not affect whether they are like radicals.

STEP 5

The fourth pair is $3 \sqrt[9]{x}$ and $5 \sqrt[3]{y}$ . These are not like radicals because both the indices (9 vs3) and the radicands ( $x$ vs $y$ ) are different.

STEP 6

Therefore, the pairs that consist of like radicals are $\sqrt[4]{5}$ and $\sqrt[4]{5}$ , and $35 \sqrt{5}$ and $y \sqrt{5}$ .

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QuestionWhich pair are like radicals? 1) 54\sqrt[4]{5}45​ and 54\sqrt[4]{5}45​ 2) 3x3 \sqrt{x}3x​ and 3x\sqrt{3 x}3x​ 3) 35535 \sqrt{5}355​ and y5y \sqrt{5}y5​ 4) 3x93 \sqrt[9]{x}39x​ and 5y35 \sqrt[3]{y}53y​

Studdy Solution

STEP 1

Assumptions1. Like radicals are radicals that have the same index and the same radicand. The index is the root number (such as the in a square root, or the3 in a cube root), and the radicand is the number under the root symbol.

STEP 2

Now, let's examine each pair to see if they are like radicals.The first pair is 54\sqrt[4]{5}45​ and 54\sqrt[4]{5}45​. These are like radicals because they have the same index (4) and the same radicand (5).

STEP 3

The second pair is 3x3 \sqrt{x}3x​ and 3x\sqrt{3 x}3x​. These are not like radicals because the radicands are different (xxx vs 3x3x3x).

STEP 4

The third pair is 3535 \sqrt{}35​ and yy \sqrt{}y​. These are like radicals because they have the same index (which is2, implied for square roots) and the same radicand (). Note that the coefficients (35 and y) do not affect whether they are like radicals.

STEP 5

The fourth pair is 3x93 \sqrt[9]{x}39x​ and 5y35 \sqrt[3]{y}53y​. These are not like radicals because both the indices (9 vs3) and the radicands (xxx vs yyy) are different.

STEP 6

Therefore, the pairs that consist of like radicals are 54\sqrt[4]{5}45​ and 54\sqrt[4]{5}45​, and 35535 \sqrt{5}355​ and y5y \sqrt{5}y5​.

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Studdy solves anything!

Start learning now

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

QuestionWhich pair are like radicals? 1) $\sqrt[4]{5}$ and $\sqrt[4]{5}$ 2) $3 \sqrt{x}$ and $\sqrt{3 x}$ 3) $35 \sqrt{5}$ and $y \sqrt{5}$ 4) $3 \sqrt[9]{x}$ and $5 \sqrt[3]{y}$

Now, let's examine each pair to see if they are like radicals.
The first pair is $\sqrt[4]{5}$ and $\sqrt[4]{5}$ . These are like radicals because they have the same index (4) and the same radicand (5).

The second pair is $3 \sqrt{x}$ and $\sqrt{3 x}$ . These are not like radicals because the radicands are different ( $x$ vs $3x$ ).

The third pair is $35 \sqrt{}$ and $y \sqrt{}$ . These are like radicals because they have the same index (which is2, implied for square roots) and the same radicand (). Note that the coefficients (35 and y) do not affect whether they are like radicals.

The fourth pair is $3 \sqrt[9]{x}$ and $5 \sqrt[3]{y}$ . These are not like radicals because both the indices (9 vs3) and the radicands ( $x$ vs $y$ ) are different.

Therefore, the pairs that consist of like radicals are $\sqrt[4]{5}$ and $\sqrt[4]{5}$ , and $35 \sqrt{5}$ and $y \sqrt{5}$ .