Answer:
[tex] \sqrt{2^{2} } * \sqrt{2^{2} } * \sqrt{2} * \sqrt{5} * \sqrt{7} * \sqrt{y^{2} } * \sqrt{y} [/tex]
[tex] 2*2*y\sqrt{2*5*7*y} [/tex]
[tex] 4y\sqrt{70y} [/tex]
Step-by-step Explanation:
To find the expressions that are equivalent to
[tex] \sqrt{1,120y^{3} } [/tex]
let's simplify each of the options given to know if we would arrive at
[tex] \sqrt{1,120y^{3} } [/tex]
Option 1:
[tex] \sqrt{2*2*2*2*5*7*y*y} [/tex]
[tex] \sqrt{(2*2*2)*(2*5)*(7)*(y*y)} [/tex]
[tex] \sqrt{8*10*7*y^{2} } [/tex]
[tex] \sqrt{560y^{2} } [/tex]
Not equivalent to the given expression.
Option 2:
[tex] \sqrt{2^{2} } * \sqrt{2^{2} } * \sqrt{2^{2} } * \sqrt{5^{2} } * \sqrt{7^{2} } * \sqrt{y^{2} } * \sqrt{y^{2} } [/tex]
[tex] 2 * 2 * 2 * 5 * 7 * y * y [/tex]
[tex] 8*5*7*y*y [/tex]
[tex] 280y^{2} [/tex]
Not equivalent to the given expression.
Option 3:
[tex] \sqrt{2^{2} } * \sqrt{2^{2} } * \sqrt{2} * \sqrt{5} * \sqrt{7} * \sqrt{y^{2} } * \sqrt{y} [/tex]
[tex] 2 * 2 * \sqrt{2} * \sqrt{5} * \sqrt{7} * y * \sqrt{y} [/tex]
[tex] 2 * 2 * y * \sqrt{2} * \sqrt{5} * \sqrt{7} * \sqrt{y} [/tex]
[tex] 4y * \sqrt{2 * 5 * 7 * y} [/tex]
[tex] \sqrt{16y^{2} } * \sqrt{70y} [/tex]
[tex] \sqrt{16 * y^{2} * 70 * y } [/tex]
[tex] \sqrt{16 * 70 * y^{2} * y } [/tex]
[tex] \sqrt{1,120y^{3} } [/tex]
This option is equivalent.
Option 4:
[tex] 2*2*y\sqrt{2*5*7*y} [/tex]
[tex] 4y\sqrt{70y} [/tex]
[tex] \sqrt{16y^{2} } * \sqrt{70y} [/tex]
[tex] \sqrt{16 * y^{2} * 70 * y } [/tex]
[tex] \sqrt{1,120y^{3} } [/tex]
This option is equivalent to the given expression.
Option 5:
[tex] 4y\sqrt{70y} [/tex]
[tex] \sqrt{16y^{2} } * \sqrt{70y} [/tex]
[tex] \sqrt{16y^{2} * 70 * y} [/tex]
[tex] \sqrt{16 * 70 * y^{2} * y} [/tex]
[tex] \sqrt{1,120y^{3} } [/tex]
Equivalent!
Options 3, 4 and 5 are the 3 expressions equivalent to
[tex] \sqrt{1,120y^{3} } [/tex]
